Physics
Reigate Grammar School
Introduction
Welcome to A-level Physics.
The course you are studying is the WJEC (Welsh Joint Education Committee) GCE Physics
(3321) course. The course homepage is at snipurl.com/2p64t. Over the next two years
you will be expanding your knowledge and extending your practical skills in Physics. The
subject matter is broken down into 6 modules:
 Motion, Energy & Charge
 Waves and Particles
 Practical Physics
 Oscillations and Fields
 Magnetism, Nuclei & Options
 Experimental Physics
The details of which can be found on pages 17 to 65.
You will receive 4½ hours of lessons a week and will be expected to do a minimum of 3
hours of work in your own time to reinforce and prepare for the work in lessons; this
includes homework. To help you with homework and to understand the material, you
have a single text book, Advanced Physics by Adams and Allday. It is substantial book
and an excellent source of information and practice questions; do not shy away from
using this book.
Throughout the course you will be doing practical work, WJEC is well known for
demanding high standards of practical work. The main emphasis of this work will be on
the analysis of data. WJEC have produced a guide which you should have with you at all
times, it can be found on pages 5 to 16.
WJEC is also known for requiring candidates to use the correct terminology when
describing physical processes. Get used to using the correct terminology when in
discussion with your teacher or fellow pupil. To help you, WJEC have created a glossary
of terms (pages 66 to 73), you must learn the meaning of these terms as well as how to
use them. There is also a table to fill in of all the quantities and units that you will use at
A level, as well as all the different types of relationship that you will be expected to plot;
these can be found on pages 74 to 85.
A level is a stepping stone from GCSE to university. You will therefore have to take much
greater responsibility for your learning. We believe that encouraging you to do some
independent learning and research is a fundamental part of your education. On page ii is
a list of skills that you need to develop over the next two years. We have also identified
the topics that naturally lend themselves to independent research; you do not need to
wait for a topic to be covered before you read about it. To help guide you to relevant
sources and mind-blowing concepts we have compiled a list of books (on page iii) which
you should read during the two year course.
At the end of 6th and 7th Forms there are Physics prizes. These are awarded to good
scientists that contribute to the science community at RGS and display an appropriate
level of excellence.
Finally: your teachers are the best resource that you have; use them.
AGM
July 2008
i
Independent Research in Physics
As an A-level student you are responsible for your own learning. This responsibility
includes reading around the subject material taught in class and going beyond the limits
of the syllabus.
We have identified key skills for AS and A2 students. Some of these should be ongoing
(like reading journals and books) whilst others might happen once a term (like writing
an article).
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Keep up with advances in Physics by reading the newspaper, Physics World, Physics
Review, New Scientist, Scientific American etc.
Keep up to date with scientific websites (see: http://www.npl.co.uk/).
Understand how Physics influences the world around us.
Critically assess an article in a scientific journal.
Write your own article for a journal or competition (see www.youngscientists.co.uk).
Read a popular science novel.
Go to Physics talks at Surrey University or Friday lunch time.
Give your own talk on a Friday lunch time.
Précis information (without plagiarising).
Efficiently present information.
Research a topic efficiently and evaluate the usefulness of resources.
Cite references correctly.
Explore different revision techniques.
Develop investigative skills.
Become an expert in one area of Physics – find your niche!
Some topics that naturally lend themselves to independent research include:
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Superconductivity and semiconductors
Wave-particle duality
Optical fibre communications
The uses of X-rays in medicine and how they are created
Lasers and their uses
Particle / high-energy physics
Astrophysics; processes within stars and their gravity
The science of earthquakes
Thermodynamics
Electrical generation and transmission
Radioactivity
We would like you to keep a scrap book to record your independent research.
We will be looking for evidence of development of these key skills in your scrapbook and
you will be asked to self assess your progress.
Independent research is key to developing an interest in science and thereby improving
UCAS applications for science and science related subjects.
ii
Book List
Annus Mirabilis
by John Gribbin and Mary Gribbin
A Briefer History of Time
by Stephen Hawking and Leonard Mlodinow
Cosmos
by Carl Sagan
The Fabric of the Cosmos
by Brian Greene
In Search of Schrödinger's Cat
by John Gribbin
The Never-Ending Days of Being Dead
by Marcus Chown
QED: The Strange Theory of Light and Matter
by Richard Feynman
Six Easy Pieces
by Richard Feynman
The Two Cultures
by C.P. Snow
The Universe: A Biography
by John Gribbin
These books are available from the Library.
iii
GCE PHYSICS
TAG FFISEG
Advanced Level / Safon Uwch
Constants, Formulae, and Mathematical Information
A clean copy of this booklet should be issued to candidates for their use during each GCE
Physics examination in the new specification. It is not to be used in legacy specification
examinations.
Centres are asked to issue this booklet to candidates at the start of the GCE Physics course to
enable them to become familiar with its contents and layout.
Fundamental Constants
Avogadro constant
Fundamental electronic charge
Mass of an electron
Molar gas constant
Acceleration due to gravity at sea level
Universal constant of gravitation
Planck constant
Speed of light in vacuo
Permittivity of free space
Permeability of free space
Stefan constant
Wien constant
Units
NA
e
me
R
g
G
h
c
o
o

W
=
=
=
=
=
=
=
=
=
=
=
=
6.02  1023 mol 1
160  1019 C
911  1031 kg
831 J mol1 K1
981 m s2
667  10-11 N m2 kg-2
663  1034 J s
300  108 m s1
885  1012 F m1
4  107 H m1
567  10-8 W m2 K-4
290  10-3 m K
T / K =  / C + 27315
1 u = 166  10-27 kg
1
AS

m
I
V
v  u  at
x
1
2
c f
Q
t
T
I  nAve
u  v  t
R
l
v 2  u 2  2ax
F = ma
W  Fx cos
E  mg h
E  12 kx 2
ay
D
d sin   n
n1v1  n2 v2
n1 sin 1  n2 sin  2
Ek max  hf  
V  E  Ir
V 
VOUT 
R
Vtotal 
VIN 
Rtotal
 or
E  12 mv 2
f

A
V
R
I
P  IV
x  ut  12 at 2
1

max  W T 1
P  A T 4
Fx  12 mv 2  12 mu 2
Efficiency 
Useful energy transfer
total energy input
 100%
Particle Physics
particle
(symbol)
charge (e)
Lepton
number
2
electron
(e)
1
1
Leptons
electron neutrino
(e)
0
1
Quarks
up (u)
down (d)
 23
 13
0
0
A2

v  r
Mr
1000
pV  nRT
a   2r
p  13  c 2
a   2 x
x  A sin(  t   )
v  A cos ( t   )
U  32 nRT

F  BIl sin  and F  Bqv sin 
M / kg 
t
k
m
T  2
k
p  mv
Q  mc
h
p

 v


c
o I
2 a
B  o nI
  AB cos 
V
Vr.m.s.  0
2
B
R
NA
W  pV
A  N
U  Q  W
Q
C
V
o A
N  N o e  t or N 
C
A  Ao e t

d
U  12 QV
No
2x
A
or A  xo
2
log e 2
T 12
E  mc 2
Q  Q0 e  RC
t
Fields
1 Q1Q2
4 0 r 2
MM
F  G 12 2
r
F
E
1
Q
40 r 2
g
GM
r2
1 Q
40 r
 GM
Vg 
r
VE 
W  qVE ,
W  mVg
Orbiting Bodies
M2
d;
M1  M 2
Centre of mass: r1 
d3
Period of Mutual Orbit: T  2
G  M1  M 2 
Options
A:
V1
N1
B: c 
C:  

V2
N2
1
 0 0
l
l
t 
;
Y
;
Q
t
  AK

x
;
X L  L ;
XC 
1
C
;
Z
X 2  R2 ;
Q
0 L
R

1
D: I  I 0 exp    x  ;
E:
I
;
t
; E  L

;

v2
c2

F
U
K
x
A
Z  c
;
U  12 V
Q2 T2

Q1 T1
Carnot efficiency 
 Q1  Q2 
Q1
3
Mathematical Information
SI Multipliers
Multiple Prefix
Symbol
Multiple
Prefix
Symbol
10-18
atto
a
103
kilo
k
10-15
femto
f
106
mega
M
10-12
pico
p
109
giga
G
10-9
nano
n
1012
tera
T
10-6
micro

1015
peta
P
10-3
milli
m
1018
exa
E
10-2
centi
c
1021
zetta
Z
Areas and volumes
Area of a circle   r 2 
d2
4
Area of a triangle = ½ base  height
;
Solid
rectangular block
Surface area
2  lh  hb  lb 
cylinder
2 r  r  h 
sphere
4 r 2
Volume
lbh
 r 2h
4
 r3
3
Trigonometry
P

R
sin  
PQ
;
PR
Q
cos 
QR
;
PR
tan  
PQ
;
QR
sin 
 tan 
cos
PR2 = PQ2 + QR2
Logarithms (A2 only)
[Unless otherwise stated, ‘log’ can be loge (i.e. ln) or log10]
log(ab)  log a  log b
log xn  n log x
log e 2  ln 2  0.693
4
a
log    log a  log b
b
loge ekx  ln ekx  kx
ADVICE FOR CANDIDATES IN PRACTICAL PHYSICS
 Before commencing any question read the whole question through completely.
 You will be allowed 15 minutes to complete each Section A question. In this time you
should complete all required calculations and written answers.
 You will be allowed 45 minutes to complete each Section B question. In this time you
should complete all required calculations and written answers.
 Where possible, repeat all readings so that you may calculate the best value and
uncertainty. If repeat readings are not required the question will state so. Record all
readings, including repeat readings, and quote the appropriate units.
 Express any answers – including the gradients and intercepts of graphs – to an
appropriate number of significant figures and with the appropriate units.
 Show all intermediate steps in calculations as credit will be given for a correct
approach even if the final answer is incorrect.
 Where the question requires it, estimate the uncertainty and/or the percentage
uncertainty in a measured or calculated quantity and express the quantity ± its
uncertainty [see below].
Graphs
 Include a title and axes which are labelled with scales and units.

Make sure the scales are convenient to use, so that readings may easily be taken from
the graph – avoid scales which use factors of 3 – and that the plotted points occupy at
least half of both the vertical and horizontal extent of the graph grid.

Draw an appropriate best-fit line; consider carefully whether the data suggest that the
appropriate line is straight or curved. Draw the appropriate line by eye rather than
calculation – though you may want to calculate the centroid of the data points.

When extracting data from a graph, use the best-fit line rather than the original data.

When determining the gradient of a graph, show clearly on your graph the readings
you use. This is most conveniently done by drawing a right angled triangle – this
should be large so that accuracy is preserved.
5
Uncertainties
1. Expressing uncertainties
Use the form x ± u, where x is the quantity being measured and u its estimated
uncertainty.
2. Estimating uncertainties using the resolution of an instrument.
If a single reading is taken and there is no reason to believe that the uncertainty is
greater, take the uncertainty to be the instrument resolution.
3. Estimating uncertainties using the spread of readings.
Take the estimated uncertainty to be half the spread in the readings, discounting any
anomalous readings.
i.e.
u
xmax  xmin
2
4. Percentage uncertainties
The percentage uncertainty, p, is calculated from:
p
Estimated uncertainty
100%
Mean value
Uncertainties in calculated quantities
1. If a quantity is calculated by multiplying and/or dividing two or more other
quantities, each of which has its own uncertainty, the percentage uncertainty is found
by adding the percentage uncertainties.
e.g. If  is calculated using  
ay
, the percentage uncertainty in  is:
D
p  pa  py  pD .
2. If a quantity is calculated by multiplying by a constant, the percentage uncertainty is
unchanged.
3. If a quantity is raised to a power, e.g. x2, x3 or x , the percentage uncertainty is
multiplied by the same power.
Example of 2 and 3: The energy, E, stored in a stretched spring is given by E  12 kx 2 . Both
k and x have uncertainties, but 12 has no uncertainty.
pE  pk  2 px
So
6
Guidance notes on experimental work.
Section 1 – Treatment of uncertainties in Physics at AS and A2 level
Preamble
One of the main aims of the practical work undertaken in GCE Physics is for candidates to
develop a feeling for uncertainty in scientific data. Some of the treatment that follows may
appear daunting. That is not the intention. The estimates of uncertainties that are required in
this specification are more in the nature of educated guesses than statistically sound
calculations.
Definitions
Uncertainty
Uncertainty in measurements is unavoidable and estimates the range within which the answer
is likely to lie. This is usually expressed as an absolute value, but can be given as a
percentage.
The normal way of expressing a measurement x0, with its uncertainty, u, is x0 ± u. This means
that the true value of the measurement is likely to lie in the range x0  u to x0 + u.
Note: The term “error” is used in many textbooks instead of uncertainty. This term implies
that something has gone wrong and is therefore best avoided.
Uncertainties can be split up into two different categories:
-
-
Random uncertainties – These occur in any measured quantity. The uncertainty of
each reading cannot be reduced by repeat measurement but the more measurements
which are taken, the closer the mean value of the measurements is likely to be to the
“true” value of the quantity. Taking repeat readings is therefore a way of reducing the
effect of random uncertainties.
Systematic uncertainties – These can be due to a fault in the equipment, or design of
the experiment e.g. possible zero error such as not taking into account the resistance
of the leads when measuring the resistance of an electrical component or use of a ruler
at a different temperature from the one at which it is calibrated. The effect of these
cannot be reduced by taking repeat readings. If a systematic uncertainty is suspected,
it must be tackled either by a redesign of the experimental technique or theoretical
analysis. An example of this sort of uncertainty, the origin of which remains
mysterious, is in the determination of stellar distances by parallax. The differences
between the distances, as determined by different observatories, often exceeds the
standard uncertainties by a large margin.
Percentage uncertainty
This is the absolute uncertainty expressed as a percentage of the best estimate of the true
value of the quantity.
Resolution
This is the smallest quantity to which an instrument can measure.
7
Mistake
This is the misreading of a scale or faulty equipment.
Anomalous points
These are points that lie well outside the normal range of results e.g. well away from a line or
curve of best fit. They often arise from mistakes in measurement. These should be recorded
and reason for discarding noted by the candidate.
How is the uncertainty in the measurement of a quantity estimated?
1. Estimation of uncertainty using the spread of repeat readings.
Suppose the value a quantity x is measured several times and a series of different
values obtained:
x1, x2, x3……..xn. [Normally, in our work, n will be a small number, say 3 or 5].
Unless there is reason to suspect that one of the results is seriously out [i.e. it is
anomalous], the best estimate of the true value of x is the arithmetic mean of the
readings:
x1  x2  ........xn
n
A reasonable estimate of the uncertainty is ½ the range:
Mean value x 
xmax  xmin
, where xmax is the maximum and xmin the minimum reading of
2
x [ignoring any anomalous readings]
i.e.
u
Example
The following results were obtained for the time it took for an object to roll down a
slope.
4.5 s, 4.8 s, 4.6 s, 5.1 s, 5.0 s
The best estimate of the true time is given by the mean which is:
t
4.5  4.8  4.6  5.1  5.0
 4.8s
5
The uncertainty, u, is given by: u 
5.1  4.5
 0.3s
2
The final answer and uncertainty should be quoted, with units, to the same no. of
decimal places and the uncertainty to 1 sig. fig
i.e. t = 4.8 ± 0.3 s
Note that, even if the initial results had be taken to the nearest 0.01 s, i.e. the
resolution of an electronic stopwatch, the final result would still be given to 0.1 s
because the first significant figure in the uncertainty is in the first place after the
decimal point.
The percentage uncertainty, p 
8
0.3
100%  6% . Again, p is only expressed to 1 s.f.
4.8
2. Estimation of uncertainty from a single reading
Sometimes there may only be a single reading. Sometimes all the readings may be
identical. Clearly it cannot be therefore assumed that there is zero uncertainty in the
reading(s).
With analogue instruments, it is not expected that interpolated readings will be taken
between divisions (this is clearly not possible with digital instrument anyway). Hence,
the uncertainty cannot be less than ½ the smallest division of the instrument being
used, and is recommended it be taken to be ± the smallest division. In some cases,
however, it will be larger than this due to other uncertainties such as reaction time [see
later] and manufacturer’s uncertainties. If other sources of random uncertainty are
present, it is expected that in most cases repeat readings would be taken and the
uncertainty estimated from the spread as above.
Advice for Specific apparatus
Metre Rule
Take the resolution as ±1 mm. This may be unduly pessimistic, especially if care is taken to
avoid parallax errors. It should be remembered that all length measurements using rules
actually involve two readings – one at each end – both of which are subject to uncertainty. In
many cases the uncertainty may be greater than this due to the difficulty in measuring the
required quantity, for example due to parallax or due to the speed needed to take the reading
e.g. rebound of a ball, in which case the precision could be ± 1 cm. In cases involving
transient readings, it is expected that repeats are taken rather than relying on a guess as to the
uncertainty.
Standard Masses
For 20g, 50g, 100g masses the precision can be taken as being as being ±1g this is probably
more accurate than the manufacturer’s [often about 3%]. Alternatively, if known, the
manufacturer’s uncertainty can be used.
Digital meters [ammeters/voltmeters]
The uncertainty can be taken as being ± the smallest measurable division. Strictly this is often
too accurate as manufacturers will quote as bigger uncertainty. [e.g. 2% + 2 divisions]
Thermometers
Standard -10 ºC to 110 ºC take precision as 1ºC
Digital thermometers uncertainty could be ± 0.1ºC. However the actual uncertainty may be
greater due to difficulty in reading a digital scale as an object is being heated or cooled, when
the substance is not in thermal equilibrium with itself let alone with the thermometer.
9
The period of oscillation of a Pendulum/Spring
The resolution of a stop watch, used for measuring a period, is usually 0.01s. Reaction time
would increase the uncertainty and, although in making measurements on oscillating
quantities it is possible to anticipate, the uncertainty derived from repeat readings is likely to
be of the order of 0.1 s. To increase accuracy, often 10 (or 20) oscillations are measured. The
absolute error in the period [i.e. time for a single oscillation] is then 1/10 (or 1/20 respectively)
of the absolute error in the time for 10 (20) oscillations
e.g. 20 oscillations: Time = 15.8 ± 0.1 s [0.6%]
15.8  0.1
 Period 
s = 0.790 ± 0.005 s
20
Note that the percentage uncertainty, p, in the period is the same as that in the overall time.
In this case, p 
0.1
100%  0.6% (1 s.f.)
15.8
Digital vernier callipers/micrometer
Precision smallest measurable quantity usually ± 0.01mm.
Measuring cylinder / beakers/ burette
Smallest measurable quantity e.g. ± 1 cm³, but this depends upon the scale of the instrument.
In the case of measuring the volume using the line on a beaker, the estimated uncertainty is
likely to be much greater.
Note candidates must be careful to avoid parallax when taking these measurements, and
should state that all readings were taken at eye level. They should also measure to the bottom
of the meniscus.
10
Determining the uncertainties in derived quantities.
Please note that candidates entered for AS award will now be required to combine
percentage uncertainties.
Very frequently in Physics, the values of two or more quantities are measured and then these
are combined to determine another quantity; e.g. the density of a material is determined using
the equation:
m

V
To do this the mass, m, and the volume, V, are first measured. Each has its own estimated
uncertainty and these must be combined to produce an estimated uncertainty in the density.
The volume itself may have been determined by combining several independent quantity
determinations [e.g. length, breadth and height for a rectangular solid or length and diameter
for a cylindrical wire].
In most cases, quantities are combined either by multiplying or dividing and this will be
considered first. Multiplying by a constant, squaring (e.g. in 34  r 3 ), square rooting or raising
to some other power are special cases of this and will be considered next.
1. Multiplying and dividing:
The percentage uncertainty in a quantity, formed when two or more quantities are
combined by either multiplication or division, is the sum of the uncertainties in the
quantities which are combined.
Example
The following results were obtained when measuring the surface area of a
glass block with a 30cm rule, resolution 0.1cm
Length = 9.7 ± 0.1 cm
Width = 4.4 ± 0.1cm
Note that these uncertainties are estimates from the resolution of the rule.
This gives the following percentage errors:
0.1
100%  1.0%
9.7
0.1
Width
pW 
100%  2.2%
4.4
So the percentage error in the volume, pV  1.0  2.2  3.2%
Hence surface area = 9.7  4.4 = 42.68 cm² ± 3.2 %
The absolute error in the surface area is now 3.2% of 42.68 = 1.37 cm²
Quoted to 1 sig. fig. the uncertainty becomes 1 cm²
The correct result, then, is 43 ± 1cm² - Note that surface area is expressed to a
number of significant figures which fits with the estimated uncertainty.
Length:
pL 
11
2. Raising to a power (eg x2, x1,
x)
The percentage uncertainty in xn is n times the percentage uncertainty in x.
e.g. a period (T) is as being 31 seconds with a percentage uncertainty of 2 %,
So T2 = 961 ± 4%.
4%  961 = 40 (to 1.s.f)
So the period squared is expressed as T2 = 960 ± 40 s.
Note: x1 is the same as 1/x. So the percentage uncertainty in 1/x is the same as that in
x. Can you see why we ignore the  sign?
Note: the percentage uncertainty in x is half the percentage uncertainty in x.
3. Multiplying by a constant
In this case the percentage uncertainty is unchanged. So the percentage uncertainty in
3x or 0.5x or x is the same as that in x.
Example: The following determinations were made in order to find the
volume of a piece of wire:
Diameter: d = 1.22 ± 0.02 mm
Length: l = 9.6 ± 0.1 cm
The percentage uncertainties are: pd = 1.6%; pl = 1.0%.
Working in consistent units, and applying the equation V 
d2
4
l , we have:
V = 448.9 mm3
The percentage uncertainty, pV = 1.6  2 + 1.0 = 4.2 % = 4 % (to 1 s.f.)
[Note that  and 4 have no uncertainties.]
So the absolute uncertainty u = 448.9  0.04 = 17.956 = 20 (1 s.f.)
So the volume is expressed as V = 450 ± 20 mm3.
4. Adding or subtracting quantities [A2 only]
If 2 quantities are added or subtracted the absolute uncertainty is added. This situation
does not arise very frequently as most equations involve multiplication and division
only. The e.m.f. / p.d. equation for a power supply is an exception.
In all cases, when the final % uncertainty is calculated it can then be converted back to an
absolute uncertainty and quoted 1 sig. figure. The final result and uncertainty should be
quoted to the same number of decimal places
12
Notes for purists:
1. When working at a high academic level, where many repeat measurements are taken,
scientists often use “standard error” , a.k.a. “standard uncertainty”. Where this is used, the
expression x0 ±  is taken to mean that there is a 67% probability that the value of x is in
the range x0   to x0 + , a 95% probability that it lies in the range x0  2 to x0 + 2, a
98% probability that it is between x0  3 and x0 + 3, etc. Our work on uncertainties will
not involve this high-level approach.
2. The method which we use here of estimating the uncertainty in an individual quantity takes
no account of the number of readings. This is because it is expected that only a small
number of readings will be taken. Detailed derivation of standard uncertainties (see above)
involves taking the standard deviation of the readings and then dividing this by n  1 , so
taking 10 readings would involve dividing  by 3.
3. The above method of combining uncertainties has the merit of simplicity but it is unduly
pessimistic. If several quantities are combined, it is unlikely that the actual error (sic) in all
of them is in the same direction, i.e. all + or all . Hence adding the percentage
uncertainties overestimates the likely uncertainty in the combination. More advanced work
involves adding uncertainties in quadrature: i.e. p  p12  p2 2  p32  ...... . This is normally
done when standard uncertainties are employed (note 1 above).
It is not intended that candidates pursue any of these courses!
13
GRAPHS [derivation of uncertainties from graphs is only expected in A2]
The following remarks apply to linear graphs:
The points should be plotted with error bars. These should be centred on the plotted point and
have a length equal to ymax  ymin [for uncertainties in the y values of the points]. If identical
results are obtained the precision of the instrument could be used. If the error bars are too
small to plot this should be stated.
If calculating a quantity such as gradient or intercept the steepest line and a least steep line
should be drawn which are consistent with the error bars. It is often convenient to plot the
centroid of the points to help this process. This is the point x, y , the mean x value against
 
the mean y value. The steepest and least steep lines should both pass through this point.
.
The maximum and minimum gradients, mmax and mmin, [or intercepts, cmax and cmin] can now
be found and the results quoted as:
mmax  mmin mmax  mmin

2
2
c c
c c
intercept = max min  max min
2
2
gradient =
Scales
Graph should cover more than ½ of the graph paper available and awkward scales [e.g.
multiples of 3] should be avoided. Rotation of the paper through /2 [90 !] may be employed
to give better coverage of the graph paper.
Semi-log and log-log graphs [A2 only]
Students will be expected to be familiar with plotting these graphs as follows:
Semi-log: to investigate relationships of the form: y  ka x .
Taking logs: log y  log k  x log a or ln y  ln k  x ln a [It doesn’t matter which]
So a plot of log y against x has a gradient log a and an intercept log k .
Examples: Radioactive or capacitor decay, oscillation damping
Log-log: to investigate relationships of the form: y  Axn
Taking logs: log y  log A  n log x [or the equivalent with natural logs]
So a plot of log y against log x has a gradient n and an intercept log A .
Examples: Cantilever depression or oscillation period as a function of overhang
length, Gallilean moon periods against orbital radius to test relationship.
Note that Log-log or semi-log graph paper will not be required.
Uncertainties from Log graphs: Candidates will not be expected to include error bars in log
plots.
14
Section 2 – Experimental techniques
The following is a selection of experimental techniques which it is anticipated that candidates
will acquire during their AS and A2 studies. It is not exhaustive, but is intended to provide
some guidance into the expectations of the PH3 and PH6 experimental tasks.
Measuring instruments
The use of the following in the context of individual experiments:
 micrometers and callipers. These may be analogue or digital. It is intended that candidates
will have experience of the use of these instruments with a discrimination of at least
0.01 mm. A typical use is the determination of the diameter of a wire.
 digital top-loading balances.
 measuring cylinders and burettes. This is largely in the context of volume and density
determination.
 force meters (Newton meters).
 stop watches with a discrimination of 0.01 s. It is also convenient to use stopwatches /
clocks with a discrimination of 1 s.
 rules with a discrimination of 1 mm.
 digital multimeters with voltage, current and resistance ranges. The following (d.c.)
ranges and discriminations illustrative the ones which are likely to be useful:
2V
0.001 V
20 V
0.01 V
10 A
0.01 A
2A
0.001 A
2 k
1
200 
0.01 
Students should be familiar with the technique of starting readings on a high range to
protect the instrument.
 liquid in glass thermometers. -10  110C will normally suffice, though candidates can be
usefully introduced to the advantages of restricted range thermometers. Where
appropriate, digital temperature probes may be used.
Experimental techniques
The purpose of PH3 is to test the ability of the candidates to make and interpret
measurements, with special emphasis on:
 combining measurements to determine derived values, eg density or internal
resistance
 estimating the uncertainty in measured and derived quantities
 investigating the relationships between variables
These abilities will be developed by centres, using all the content of PH1 and PH2. They can
and will be assessed using very simple apparatus which can be made available in multiple
quantities. Hence it is not foreseen that apparatus which centres are likely to possess in small
numbers, if at all, will be specified, e.g. oscilloscopes, data loggers, travelling microscopes.
15
The following list may be found useful as a checklist. Candidates should be familiar with the
following techniques:
 connecting voltmeters across the p.d. to be determined, i.e. in parallel;
 connecting ammeters so that the current flows through them, i.e. in series;
 the need to avoid having power supplies in circuits when a resistance meter is being
employed;
 taking measurements of diameter at various places along a wire / cylinder and taking
pairs of such measurements at right angles to allow for non-circular cross sections;
 determining a small distance measurement, e.g. the thickness or diameter of an object,
by placing a number of identical objects in contact and measuring the combined
value, e.g. measuring the diameter of steel spheres by placing 5 in line and measuring
the extent of the 5;
 the use of potentiometers (N.B. not metre wire potentiometers) and variable resistors
in circuits when investigating current-voltage characteristics;
 the determination of the period and frequency of an oscillating object by determining
the time taken for a number of cycles [typically 10 or 20]; N.B. Although the concept
of period is not on the AS part of the specification, it is likely to be used in PH3;
 the use of fiducial marks and no-parallax in sighting against scales and in period
determinations.
16
SUMMARY OF ASSESSMENT
This specification is divided into a total of 6 units: 3 AS units and 3 A2 units. Weightings
noted below are expressed in terms of the full A level qualification.
AS (3 units)
PH1
20% 1¼ hour Written Paper 80 marks[120 UM]
Motion, Energy & Charge
Approx 7 structured questions. No question choice. No sections.
PH2
20% 1¼ hours Written Paper 80 marks [120 UM]
Waves & Particles
Approx 7 structured questions. No question choice. No sections.
PH3
10% Internal Assessment 48 marks [60 UM]
Practical Physics
Experimental tasks, performed under controlled conditions, based upon
experimental techniques developed in the AS course.
A LEVEL (the above plus a further 3 units)
PH4
18% 1¼ hour Written Paper 80 marks [108 UM]
Oscillations & Fields
Approx 7 questions. Includes synoptic assessment. No question choice.
No sections.
PH5
22% 1¾ hour written paper 100 marks[132 UM]
Electromagnetism, Nuclei and Options
Section A: Approximately 5 questions on the compulsory content of the
unit. 60 marks
Section B: Case Study, synoptic in nature, based upon open-source
material distributed by the board. 20 marks
Section C: Options: Alternating Currents, Revolutions, Materials,
Medical Physics, Energy. 20 marks
PH6
10% Internal Assessment [UMS = 60]
Experimental & Synoptic Assessment
An experimental task (25 marks), and a data-analysis task (25 marks)
performed under controlled conditions, both synoptic in nature.

Synoptic assessment is included in PH4 and PH5. It is inherent in the internal assessment PH6
17
PHYSICS
1
INTRODUCTION
1. 1
Criteria for AS and A Level GCE
This specification has been designed to meet the general criteria for GCE Advanced
Subsidiary (AS) and A level (A) and the subject criteria for AS/A Physics as issued by the
regulators [July 2006]. The qualifications will comply with the grading, awarding and
certification requirements of the Code of Practice for 'general' qualifications (including GCE).
The AS qualification will be reported on a five-grade scale of A, B, C, D, E. The A level
qualification will be reported on a six-grade scale of A*, A, B, C, D, E. The award of A* at A
level will provide recognition of the additional demands presented by the A2 units in term of
'stretch and challenge' and 'synoptic' requirements. Candidates who fail to reach the minimum
standard for grade E are recorded as U (unclassified), and do not receive a certificate. The
level of demand of the AS examination is that expected of candidates half way through a full
A level course.
The AS assessment units will have equal weighting with the second half of the qualification
(A2) when these are aggregated to produce the A level award. AS consists of three assessment
units, referred to in this specification as PH1, PH2 and PH3. A2 also consists of three units,
referred to as PH4, PH5 and PH6.
Assessment units may be retaken prior to certification for the AS or A level qualifications, in
which case the better result will be used for the qualification award. Individual assessment
unit results, prior to certification for a qualification, have a shelf-life limited only by the shelflife of the specification.
The specification and assessment materials are available in English and Welsh.
1.2
Progression
This specification provides a suitable foundation for the study of Physics, Engineering,
Medicine or a related area through a range of higher education courses or direct entry into
employment. In addition, the specification provides a coherent, satisfying and worthwhile
course of study for candidates who do not progress to further study in this subject.
19
1.3
Rationale
The specification for AS and A-level Physics complies with the GCE AS and A Subject
Criteria for Science Subjects, published by CCEA, DELLS and QCA. It provides
(a)
a complete course in Physics to GCE A level;
(b)
a firm foundation in Physics knowledge and understanding, together with
mathematical competence for those wishing proceed to further studies in Physics,
Engineering, Mathematics, Medicine or the Natural Sciences.
Students who follow the specification will be introduced to a wide range of Physics principles
and be led to an understanding of how nature operates at both microscopic and macroscopic
scales. They will understand how these principles are applied in tackling problems of human
society.
1.4
The Wider Curriculum
Physics is a subject that by its nature requires candidates to consider individual, ethical,
social, cultural and contemporary issues. The specification provides a framework for
exploration of such issues and includes specific content through which educators may address
these issues; for example, the use of radioactive isotopes in medicine, the discussion on
nuclear power and the environmental consequences of the use of fossil fuels.
The specification contains topics which allow teachers within Wales to draw upon Welsh
examples and priorities in line with the Curriculum Cymreig, for example in the development
of energy resources.
1.5
Equality and Fair Assessment
AS/A levels often require assessment of a broad range of competences. This is because they
are general qualifications and, as such, prepare candidates for a wide range of occupations and
higher level courses.
The revised AS/A level qualification and subject criteria were reviewed to identify whether
any of the competences required by the subject presented a potential barrier to any disabled
candidates. If this was the case, the situation was reviewed again to ensure that such
competences were included only where essential to the subject. The findings of this process
were discussed with disability groups and with disabled people.
In GCE Physics practical assistants may be used for manipulating equipment and making
observations. Technology may help visually impaired students to take readings and make
observations.
Reasonable adjustments are made for disabled candidates in order to enable them to access
the assessments. For this reason, very few candidates will have a complete barrier to any part
of the assessment. Information on reasonable adjustments is found in the Joint Council for
Qualifications document Regulations and Guidance Relating to Candidates who are eligible
for Adjustments in Examinations. This document is available on the JCQ website
(www.jcq.org.uk).
Candidates who are still unable to access a significant part of the assessment, even after
exploring all possibilities through reasonable adjustments, may still be able to receive an
award. They would be given a grade on the parts of the assessment they have taken and there
would be an indication on their certificate that not all of the competences have been
addressed. This will be kept under review and may be amended in future.
20
2
AIMS
The AS and A specifications in Physics aim to encourage students to:
(a)
develop an enthusiasm for Physics and, where appropriate to pursue this enthusiasm
in its further study;
(b)
understand the processes of Physics, as a Natural Science, the way the subject
develops through experiment, theory, insight and creative thought;
(c)
appreciate the role of Physics in society, in particular how its discoveries are applied
in industry and medicine and how decisions about its use are made;
(d)
appreciate the interconnectedness of the subject and the ways in which different
strands of Physics can be used to solve problems and gain new insights into the
natural world;
(e)
acquire a more general understanding of the way in which scientific disciplines make
progress, acquire and interpret evidence, propose and evaluate solutions,
communicate ideas and interact with society, as outlined in section 3.6, How Science
Works, of the GCE AS and A level criteria for Science Subjects.
How science Works
In the context of AS/A Physics, candidates should:

use theories, models and ideas to develop and modify scientific explanations;

use knowledge and understanding to pose scientific questions, define scientific
problems, present scientific arguments and scientific ideas;

use appropriate methodology, including ICT, to answer scientific questions and solve
scientific problems;

carry out experimental and investigative activities, including appropriate risk
management, in a range of contexts;

analyse and interpret data to provide evidence, recognising correlations and causal
relationships;

evaluate methodology, evidence and data, and resolve conflicting evidence;

appreciate the tentative nature of scientific knowledge;

communicate information and ideas in appropriate ways using appropriate
terminology;

consider applications and implications of science and appreciate their associated
benefits and risks;

appreciate the role of the scientific community in validating new knowledge and
ensuring integrity;

appreciate the ways in which society uses physics knowledge and practice to inform
decision-making.
21
3
ASSESSMENT OBJECTIVES
Weightings
Assessment objective weightings are shown below as % of the full A level, with AS
weightings in brackets.
Unit
PH1
PH2
PH3
PH4
PH5
PH6
Total AS%
Total A2%
Total A%
22
Unit total
80
80
48
80
100
50
raw marks
AO1
AO2
35
35
35
35
4
4
30
40
34
60
5
5
37
30
34
37
46
42
AO3
10
10
40
10
6
40
27
23
25
unit %
weighting
20 (40)
20 (40)
10 (20)
18
22
10
4
SPECIFICATION CONTENT
4.1
Units
SI units will be used throughout this specification.
Knowledge of SI multipliers will be required. A table of the
SI multipliers will be included in each examination paper.
4.2
Practical Work
Practical work will play an important role throughout the
course. Attention is drawn to the specified content in each
unit and the instructions relating to the practical internal
assessments.
4.3
Mathematical
requirements
The following list of requirements is taken from the GCE AS
and A level Criteria for Science Subjects [July 2006]. The
sections in bold type [i.e. use of radians, the exponential and
log functions] will not be required at AS level, because the
subject content which requires these concepts is not met in
this part of the course.
Candidates will be required to:
4.3.1
Computation

recognise and use expressions in decimal and standard form

use ratios, fractions and percentages

use calculators to find and use power, exponential and logarithmic
functions

use calculators to handle sin x, cos x, tan x when x is expressed in
degrees or radians
4.3.2
Handling data

use an appropriate number of significant figures

find arithmetic means

make order of magnitude calculations.
4.3.3
Algebra

understand and use the symbols: =, <, <<, >>,>, , ~

change the subject of an equation

substitute numerical values into algebraic equations using appropriate
units for physical quantities

solve simple algebraic equations
23
4.3.4
Graphs

translate information between graphical, numerical and algebraic
forms

plot two variables from experimental or other data

understand that y = mx + c represents a linear relationship

determine the slope and intercept of a linear graph

draw and use the slope of a tangent to a curve as a measure of rate of
change

understand the possible physical significance of the area between a
curve and the x axis and be able to calculate it or measure it by
counting squares as appropriate

use logarithmic plots to test exponential and power law
variations

sketch simple functions including y = k/x, y = kx2, y = k/x2,
y = sin x, y = cos x, y = e-x
4.3.5
Geometry and Trigonometry

calculate areas of triangles, circumferences and areas of circles,
surface areas and volumes of rectangular blocks, cylinders and
spheres

use Pythagoras' theorem, and the angle sum of a triangle

use sin, cos and tan in physical problems

understand the relationship between degrees and radians and
translate from one to the other.
Advanced Subsidiary
PH1 Assessment Unit – MOTION, ENERGY & CHARGE
The Unit is built around a core relating to the following Subject Criteria content:
S3.3 (a) – (d)
S4.4(a) – (d)
Mechanics
Electrical Circuits
SPECIFICATION
PH1.1 BASIC PHYSICS
Content






Units and dimensions
Scalar and vector quantities
Force
Free body diagrams
Movements and stability
Equilibrium
AMPLIFICATION OF CONTENT
Candidates should be able to:
24
(a)
recall and use SI units,
(b)
check equations for homogeneity using units,
(c)
contrast scalar and vector quantities and give examples of each –
displacement, velocity, acceleration, force, speed, time, density,
pressure etc.,
(d)
appreciate the concept of force and understand Newton's 3rd law of
motion,
(e)
use free body diagrams to represent forces on a particle or body,
(f)
recall and use the relationship F = ma in situations where mass is
constant,
(g)
add and subtract coplanar vectors, and perform mathematical
calculations limited to two perpendicular vectors,
(h)
resolve a vector into two perpendicular components,
(i)
understand the concept of density, use the equation  
m
V
to
calculate mass, density and volume;
(j)
understand and define the turning effect of a force;
(k)
recall and use the principle of moments;
(l)
understand and use centre of gravity, for example in simple problems
including toppling and stability. Identify its position in a cylinder,
sphere and cuboid (beam) of uniform density;
(m)
understand that a body is an equilibrium when the resultant force is
zero and the net moment is zero, and be able to perform simple
calculations.
PH1.2 KINEMATICS
Content

Rectilinear motion.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
define displacement, mean and instantaneous values of speed,
velocity and acceleration,
(b)
use graphical methods to represent displacement, speed, velocity and
acceleration,
(c)
understand and use the properties of displacement-time graphs,
velocity-time graphs, acceleration-time graphs, and interpret speed
and displacement-time graphs for non-uniform acceleration,
(d)
derive and use equations which represent uniformly accelerated
motion in a straight line,
25
(e)
describe the motion of bodies falling in a gravitational field with and
without air resistance  terminal velocity,
(f)
recognise and understand the independence of vertical and horizontal
motion of a body moving freely under gravity,
(g)
describe and explain motion due to a uniform velocity in one
direction and uniform acceleration in a perpendicular direction, and
perform simple calculations.
PH1.3 ENERGY CONCEPTS
Content
•
Work, Power and Energy.
AMPLIFICATION OF CONTENT
Candidates should be able to:
26
(a)
recall the definition of work as the product of a force and distance
moved in the direction of the force when the force is constant;
calculation of work done, for constant forces, when force is not along
the line of motion ( W.D.  Fx cos )
(b)
understand that the work done by a varying force is the area under
the Force-distance graph,
(c)
recall and use Hooke's law F = kx, and apply this to (b) above to
show that elastic potential energy is 1 2 Fx or 1 2 kx2,
(d)
understand and apply the work – energy relationship
Fs  12 mv 2  12 mu 2 and recall that Ek = 12 mv2,
(e)
recall and apply the principle of conservation of energy including use
of gravitational potential energy mgh , elastic potential energy
1 kx2, and kinetic energy 1 mv2,
2
2
(f)
define power as the rate of energy transfer,
(g)
appreciate that dissipative forces e.g. friction, viscosity, cause energy
to be transferred from a system and reduce the overall efficiency of
the system,
(h)
recall and use Efficiency =
Useful energy obtained
 100%,
Energy input
PH1.4 CONDUCTION OF ELECTRICITY
Content



Electric charge.
Electric current.
Nature of charge carriers in conductors.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
understand how attraction and repulsion between rubbed insulators
can be explained in terms of charges on the surfaces of these
insulators, and that just two sorts of charge are involved;
(b)
understand that the name negative charge was arbitrarily given to the
sort of charge on an amber rod rubbed with fur, and positive to that
on a glass rod rubbed with silk;
(c)
recall that electrons can be shown to have a negative charge, and
protons, a positive;
(d)
explain frictional charging in terms of electrons removed from, or
added to, surface atoms;
(e)
recall that the unit of charge is the coulomb (C), and that an electron's
charge, e, is a very small fraction of a coulomb;
(f)
recall that charge can flow through certain materials, called
conductors;
(g)
understand that electric current is rate of flow of charge;
(h)
recall and use the equation I 
(i)
recall that current is measured in ampère (A), where A = Cs-1;
(j)
understand and describe the mechanism of conduction in metals as
the drift of free electrons;
(k)
derive and use the equation I = nAve for free electrons.
Q
t
;
27
PH1.5 RESISTANCE
CONTENT






Relationship between current and potential difference.
Resistance
Resistivity.
Variation of resistance with temperature for metals.
Superconductivity
Heating effect of an electric current.
AMPLIFICATION OF CONTENT
Candidates should be able to:
28
(a)
define potential difference and recall that its unit is the volt (V)
where V = JC-1.
(b)
sketch I – V graphs for a semiconductor diode, the filament of a
lamp, and a metal wire at constant temperature;
(c)
state Ohm's Law;
(d)
define resistance;
(e)
recall that the unit of resistance is the ohm (Ω), where Ω = VA-1;
(f)
understand that collisions between free electrons and ions give rise to
electrical resistance, and to a steady drift velocity under a given p.d.,
(g)
recall and use R 
(h)
describe how to determine the resistivity of a metal experimentally;
(i)
describe how to investigate experimentally the variation of resistance
with temperature of a metal wire;
(j)
recall that the resistance of metals varies almost linearly with
temperature over a wide range;
(k)
understand what is meant by superconductivity, and superconducting
transition temperature;
(l)
recall that not all metals show superconductivity, and that, for those
that do, the transition temperatures are a few degrees above absolute
zero (–273°C);
(m)
recall that certain special materials (high temperature
superconductors) have transition temperatures above the boiling
point of nitrogen (–196°C), and can therefore be kept below their
transition temperatures using liquid nitrogen;
l
and understand that this is the defining
A
equation for resistivity;
(n)
recall that superconducting magnets are used in particle accelerators,
tokamaks and magnetic resonance imaging machines, and are
expected soon to be used in some large motors and generators;
(o)
understand that ordinarily (that is, above the transition temperature),
collisions between free electrons and ions in metals increase the
random vibration energy of the ions, so the temperature of the metal
increases;
V2
recall and use P  IV  I 2 R 
.
R
(p)
PH1.6 D.C. CIRCUITS
CONTENT




Series and parallel circuits.
Combination of resistors.
The internal resistance of sources.
The potential divider.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
understand and recall that the current from a source is equal to the
sum of the currents in the separate branches of a parallel circuit, and
that this is a consequence of conservation of charge;
(b)
understand and recall that the p.d.s across components in a series
circuit is equal to the p.d. across the supply, and that this is a
consequence of conservation of energy;
(c)
understand and recall that the p.d.s across components in parallel are
equal;
(d)
recall and use formulae for the combined resistance of resistors in
series and parallel;
(e)
derive and use the potential divider formula
(f)
define the e.m.f. of a source and appreciate that its unit, the volt (V),
is the same as that of potential difference.
(g)
appreciate that sources have internal resistance and use the formula
V = E − Ir
(h)
calculate current and p.d.s in a simple circuit containing one cell or
cells in series.
V 
VOUT 
R
;
 or

Vtotal 
VIN  Rtotal
29
PH2 Assessment Unit – WAVES & PARTICLES
The Unit is contains the following Subject Criteria content:
3.5
3.7 (a) – (b)
Waves
Quantum physics: photons, particles
SPECIFICATION
PH2.1 WAVES
Content








Progressive waves.
Transverse and longitudinal waves.
Polarisation.
Frequency, wavelength and velocity of waves.
Diffraction.
Interference.
Two-source interference patterns.
Stationary waves.
AMPLIFICATION OF CONTENT
Candidates should be able to:
30
(a)
understand that a progressive wave transfers energy or information
from a source to a detector without any transfer of matter;
(b)
distinguish between transverse and longitudinal waves,
(c)
describe experiments which demonstrate the polarisation of light and
microwaves;
(d)
explain the terms displacement, amplitude, wavelength, frequency,
period and velocity of a wave,
(e)
draw and interpret graphs of displacement against time, and
displacement against position for transverse waves only,
(f)
recall and use the equation c = f,
(g)
be familiar with experiments which demonstrate the diffraction of
water waves, sound waves and microwaves, and understand that
significant diffraction only occurs when  is of the order of the
dimensions of the obstacle or slit,
(h)
state, explain and use the principle of superposition,
(i)
describe an experimental demonstration of two-source interference
for light, appreciating the historical importance of Young's
experiment, and be familiar with experiments which demonstrate two
source interference for water waves, sound waves and microwaves;
(j)
use the equation  
(k)
show an understanding of path difference, phase difference, and
coherence,
(l)
state the conditions necessary for two-source interference to be
observed, i.e. constant phase difference, vibrations in the same line,
(m)
recall the shape of the intensity pattern from a single slit and its effect
on double-slit and diffraction grating patterns,
(n)
use the equation d sin  = n for a diffraction grating,
(o)
give examples of coherent and incoherent sources,
(p)
describe experiments which demonstrate polarisation of light,
(q)
be familiar with experiments which demonstrate stationary waves,
e.g. vibrations of a stretched string and for sound in air,
(r)
state the differences between stationary and progressive waves,
(s)
understand that a stationary wave can be regarded as a superposition
of two progressive waves of equal amplitude and frequency,

travelling in opposite directions and that the internodal distance is
2
ay
for double-slit interference,
D
PH2.2 REFRACTION OF LIGHT
Content
•
•
•
Refraction.
Wave Model of Refraction
Optical Fibre Communications
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall and use Snell's Law of refraction;
(b)
recall and use the equations
n1v1  n2 v2
(c)
and
n1 sin 1  n2 sin  2 ;
understand how Snell's Law relates to the wave model of light
propagation;
31
(d)
understand the conditions for total internal reflection and derive and
use the equation for the critical angle
n1 sin c  n2 ;
(e)
apply the concept of total internal reflection to multimode optical
fibres;
(f)
appreciate the problem of multi-mode dispersion with optical fibres
in terms of limiting the rate of data transfer and transmission
distance;
(g)
explain how the introduction of monomode optical fibres has allowed
for much greater transmission rates and distances;
(h)
compare optical fibre communications to terrestrial microwave links,
satellite links and copper cables for long distance communication.
PH2.3 PHOTONS
Content








The photoelectric effect.
Photons
The electromagnetic spectrum
Line emission and line absorption spectra
X-rays
Spontaneous and stimulated emission
Lasers – energy levels and structure
The semiconductor laser and its uses
AMPLIFICATION OF CONTENT
Candidates should be able to:
32
(a)
describe how the photo-electric effect can be demonstrated
(b)
describe how the maximum kinetic energy, KEmax, of emitted
electrons can be measured, using a vacuum photocell;
(c)
sketch a graph of KEmax against frequency of illuminating radiation;
(d)
understand and recall how a photon picture of light leads to Einstein's
equation, Ekmax  hf   and how this equation correlates with the
graph of Ekmax against frequency;
(e)
describe in outline how X-rays are produced in an X-ray tube, and
sketch a graph of intensity against wavelength;
(f)
recall the characteristic properties and orders of magnitude of the
wavelengths of the radiations in the electromagnetic spectrum;
(g)
calculate typical photon energies for these radiations;
(h)
understand in outline how to produce line emission and line
absorption spectra from atoms;
(i)
describe the appearance of such spectra as seen in a diffraction
grating;
(j)
understand and use atomic energy level diagrams, together with the
photon hypothesis, to explain line emission and line absorption
spectra;
(k)
calculate ionisation energies from an energy level diagram;
(l)
understand and explain the process of stimulated emission and how
this process leads to light emission that is coherent;
(m)
understand the concept of population inversion (Note: for A level
students the condition N2 > N1 will suffice) and explain that
population inversion is necessary for a laser to operate;
(n)
understand that population inversion is not (usually) possible with a
2-level energy system;
(o)
understand how population inversion is attained in 3 and 4-level
energy systems;
(p)
understand the process of pumping and its purpose;
(q)
recall the structure of a typical laser i.e. an amplifying medium
between two mirrors, one of which partially transmits light;
(r)
know the basic structure of a semiconductor diode laser;
(s)
know that laser systems are far less than 1% efficient in general
(usually around 0.01% efficient) due to pumping losses but that
semiconductor lasers can obtain 70% efficiency and that pumping
requires the application of a p.d. of around 3V;
(t)
know the advantages and uses of a semiconductor laser i.e. small,
cheap, efficient and used for CDs, DVDs, telecommunication etc.
33
PH2.4 MATTER, FORCES AND THE UNIVERSE.
Content




The nuclear atom
Leptons and Quarks
Particle interactions
Conservation Laws
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
describe a simple model for the nuclear atom in terms of nucleus and
electrons orbiting in discrete orbits, explaining the composition of the
nucleus in terms of protons and neutrons and expressing the nuclear
and atomic structures using the ZA X notation
(b)
recall that matter is composed of quarks and leptons – the following
information will be available to candidates in examinations:
particle
(symbol)
Leptons
electron neutrino
electron (e)
(e)
up
(u)
Quarks
down
(d)
 23
 13
charge (e)
0
1
[N.B. No questions will be set involving generations higher than
generation 1.]
(c)
recall that antiparticles exist to the particles given in the table above,
that the properties of an antiparticle are identical to that of its
corresponding particle apart from having opposite charge, and that
particles and antiparticles annihilate; use the above table to give the
symbols of the antiparticles;
(d)
recall the following information about the four forces or interactions,
which are experienced by particles:
Interaction
34
Experienced
by
Range
Gravitational
all particles
infinite
Weak
all particles
very short
range
Electromagnetic
all charged
particles
infinite
Strong
quarks
short range
Comments
very weak – negligible
except in the context of
large objects such as
planets and stars
only significant in cases
where the electromagnetic
and strong interactions do
not operate
also experienced by neutral
hadrons because they are
composed of quarks
experienced by quarks and
particles composed of
quarks
(e)
recall that quarks are never observed in isolation, but bound into
composite particles called hadrons, which are classified as either
baryons (e.g. the proton or neutron) which consist of 3 quarks or
mesons (e.g. pions) which consist of a quark-antiquark pair;
(f)
use tables of data to suggest the quark structure of given baryons or
mesons;
(g)
understand that, in particle interactions, charge and lepton number are
conserved.
PH2.5 USING RADIATION TO INVESTIGATE STARS
Content





Black-body radiation
Wien's displacement law – stellar temperatures
Stefan's law and stellar luminosity
Intensity and the inverse square law
Fraunhofer lines and stellar composition
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall that a stellar spectrum consist of a continuous emission
spectrum, from the dense gas of the surface of the star, and a line
absorption spectrum arising from the passage of the emitted
electromagnetic radiation through the tenuous atmosphere of the star,
(b)
recall that bodies which absorb all incident radiation are known as
black bodies and that stars are very good approximations to black
bodies,
(c)
recall the shape of the black body spectrum and that the peak
wavelength is inversely proportional to the absolute temperature
(defined by T/K = /C + 27315) – Wien's displacement law;
(d)
use Wien's displacement law, Stefan's Law and the inverse square law
to investigate the properties of stars – luminosity, size, temperature
and distance [N.B. stellar brightness in magnitudes will not be
required];
(e)
interpret data on stellar line spectra to identify elements present in
stellar atmospheres;
(f)
recall that the analysis of stellar spectra reveals that roughly 75% of
the universe, by mass, is Hydrogen and 24% Helium, with very small
quantities of the other elements;
35
(g)
recall the main branch of the proton-proton chain, which is th e
main energy production mechanism in stars like the Sun:
p  p  d  e+  νe
(where d  deuteron 21 H)
p  d  23 He  γ
(where γ  photon)
3
2
He  23 He  42 He  p  p
and that neutrinos from the first step of this chain can be detected on
Earth;
36
PH3 Internal Assessment Unit – PRACTICAL PHYSICS
This Unit gives candidates opportunities to demonstrate development of their
experimental, manipulative, interpretative and communication skills.
SPECIFICATION
Candidates are required to undertake, under controlled conditions, a set of
experimental tasks. The tasks are devised by the WJEC and assessed by the
supervisor using a marking scheme provided by the WJEC.
AMPLIFICATION OF CONTENT
Candidates should be able to:
•
follow instructions and plan experimental activities,
•
make observations and draw conclusions,
•
take measurements and record data showing awareness of the limits
of accuracy and correct use of significant figures,
•
assess the uncertainty in measurements and derived quantities,
•
present data in different forms, including graphically,
•
analyse and interpret data, demonstrating appropriate knowledge and
understanding of physics, and investigate the relationships between
physical quantities,
•
evaluate experimental techniques and outcomes,
•
communicate experimental findings clearly using SI units.
Task details
•
Measuring instrument requirements will include items expected to be
found in a school laboratory [see section 8 – Guidance on Internal
Assessment].
•
Other equipment requirements will include standard laboratory items
such as clamp stands and slotted masses, but may also include items
which need to be obtained specially for the assessment from
equipment suppliers or D.I.Y. stores.
•
Detailed requirements for the assessment will be issued to centres
two months prior to the assessment. The information provided will
give the context of the task and detailed instructions on measuring
instruments required, and assemblage of apparatus.
37
•
The assessment is in two sections: Section A and Section B.
Section A consists of 3 short items, each of duration 15 minutes.
These items concentrate on making measurements, determining the
magnitude of quantities and the associated uncertainty. The contexts
are from across the AS specification. The 3 items each carry 8 marks.
Section B consists of a single item of duration 45 minutes.
Candidates are expected to undertake an investigation into the
relationship between quantities. Section B carries 24 marks.
There is no requirement for candidates to undertake the items in any
specific order.
38
•
Centres are free to organise the progression of candidates between
the items as they wish, but the timings lend themselves to assessing
candidates in multiples of 6, with 3 candidates being engaged in
Section A [tackling the items in a cycle] and 3 in Section B at any
one time.
•
Centres are issued with a marking scheme for the assessment of
candidates’ responses. The results should be forwarded to the WJEC
and the candidates’ work presented for moderation in line with the
procedures of the WJEC.
Advanced Level
PH4 Assessment Unit – OSCILLATIONS & FIELDS
Advanced Level A2
The Unit is built around a core relating to the following Subject Criteria content:
3.3 (e) – (g)
3.6
3.8 (a)
Mechanics: momentum, circular motion, oscillations
Matter: molecular kinetic theory, internal energy
Fields: force fields
SPECIFICATION
PH4.1 VIBRATIONS
Content
•
Circular motion
•
Physical and mathematical treatment of undamped simple harmonic
motion.
•
Energy interchanges during simple harmonic motion.
•
Damping of oscillations.
•
Free oscillations, forced oscillations and resonance.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
understand and use period of rotation, frequency, the radian measure
of angle,
(b)
define and use angular velocity  ,
(c)
recall and use v  r , and hence a   2 r ,
(d)
define simple harmonic motion as a statement in words,
(e)
recall, recognise and use a   2 x as a mathematical defining
equation of simple harmonic motion,
(f)
illustrate, and interpret graphically, the variation of acceleration with
displacement during simple harmonic motion,
(g)
2
recall and use x  A sin(  t   ) as a solution to a   x ,
39
(h)
explain the terms frequency, period, amplitude and phase ( t   ) ,
(i)
recall and use the period as
(j)
1
2
,
or
f

recall and use v  A cos ( t   ) for the velocity during simple
harmonic motion,
(k)
illustrate, and interpret graphically, the changes in displacement and
velocity with time during simple harmonic motion,
(l)
recall and use the equation T  2
m
for the period of a system
k
having stiffness (force per unit extension) k and mass m,
(m)
illustrate, and interpret graphically, the interchange between kinetic
energy and potential energy during undamped simple harmonic
motion, and perform simple calculations on energy changes,
(n)
explain what is meant by free oscillations and understand the effect
of damping in real systems,
(o)
describe practical examples of damped oscillations, and the
importance of critical damping in appropriate cases such as vehicle
suspensions,
(p)
explain what is meant by forced oscillations and resonance, and
describe practical examples,
(q)
sketch the variation of the amplitude of a forced oscillation with
driving frequency and know that increased damping broadens the
resonance curve,
(r)
appreciate that there are circumstances when resonance is useful e.g.
circuit tuning, microwave cooking and other circumstances in which
it should be avoided e.g. bridge design.
PH4.2 MOMENTUM CONCEPTS
Content
•
•
•

Linear momentum.
Newton's laws of motion.
Conservation of linear momentum; particle collision.
The momentum of a photon
AMPLIFICATION OF CONTENT
Candidates should be able to:
40
(a)
define linear momentum as the product of mass and velocity,
(b)
recall Newton's laws of motion and know that force is rate of change
of momentum, applying this in situations where mass is constant,
(c)
state the principle of conservation of momentum and use it to solve
problems in one dimension involving elastic collisions (where there
is no loss of kinetic energy) and inelastic collisions (where there is
loss of kinetic energy).
(d)
use the formula for the momentum of a photon: p 
(e)
appreciate that the absorption or reflection of photons gives rise to
radiation pressure.
h


hf
;
c
PH4.3 THERMAL PHYSICS
Content







Ideal gas laws and the equation of state.
Kinetic theory of gases.
The kinetic theory of pressure of a perfect gas
Internal energy.
The internal energy of an ideal gas
Energy transfer.
First law of thermodynamics.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall and use Boyles law for an ideal gas,
(b)
recall and use the equation of state for an ideal gas expressed
as pV = nRT where R is the molar gas constant, and understand that
this equation can be used to define the Kelvin scale of temperature
and the absolute zero of temperature,
(c)
recall the assumptions of the kinetic theory of gases which includes
the random distribution of energy among the particles,
(d)
explain how molecular movement causes the pressure exerted by a
gas, and understand and use p  13  c 2 
1
3
N
mc 2 where N is the
V
number of molecules,
(e)
define the Avogadro constant NA and hence the mole;
(f)
understand that the molar mass M is related to the relative molecular
mass Mr by M/kg = Mr/1000, and that the number of moles n is given
by
Total mass
;
Molar mass
41
(g)
compare pV  13 Nmc 2 with pV = nRT and deduce that the total
translational kinetic energy of a mole of a monatomic gas is given by
3
and hence the average kinetic energy of a molecule is 23 kT
2 RT

R 
 is the Boltzmann constant, and deduce that T is
where k  
 NA 
proportional to the mean kinetic energy
42
(h)
understand that the internal energy of a system is the sum of the
potential and kinetic energies of its molecules;
(i)
understand that the internal energy of an ideal monatomic gas is
wholly kinetic so is given by U  32 nRT
(j)
understand that heat enters or leaves a system through its boundary or
container wall, according to whether the system's temperature is
lower or higher than that of its surroundings, so heat is energy in
transit and not contained within the system;
(k)
understand that if no heat flows between systems in contact, then
they are said to be in thermal equilibrium, and are at the same
temperature;
(l)
understand that energy can also enter or leave a system by means of
work, so work is also energy in transit;
(m)
use W  pV to calculate the work done by a gas under constant
pressure;
(n)
understand and explain that, even if p changes, W is given by the area
under the p – V graph;
(o)
recall and use the first law of thermodynamics, in the form
U  Q  W , knowing how to interpret negative values of U, Q,
and W.
(p)
understand that for a solid (or liquid), W is usually negligible, so
Q  U ;
(q)
use the formula Q  mc , for a solid or liquid, understanding that
this is the defining equation for specific heat capacity, c.
PH4.4 ELECTROSTATIC AND GRAVITATIONAL FIELDS OF FORCE
Content
•
•
•
•
•
•
•.
•
•
Electrostatic and gravitational fields.
Field strength (intensity).
Electrical and gravitational inverse square laws.
Potential in force fields.
Relation between force and potential energy gradient.
Relation between intensity and potential gradient
Field lines and equipotential surfaces.
Vector addition of electric fields.
Potential energy of a system of charges.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall the main features of electric and gravitational fields as
specified in the table overleaf,
(b)
recall that the gravitational field outside spherical bodies such as the
earth is essentially the same as if the whole mass were concentrated
at the centre
(c)
understand that field lines (or lines of force) give the direction of the
field at a point, thus, for a positive point charge, the field lines are
radially outward; and that equipotential surfaces join points of equal
potential and are therefore spherical for a point charge
(d)
calculate the net potential and resultant field strength for a number of
point charges and point masses,
(e)
appreciate that ΔUP = mgΔh for distances over which the variation of
g is negligible.
43
REQUIREMENT
Define …
ELECTRIC FIELDS
GRAVITATIONAL FIELDS
electric field strength, E, as the force per unit gravitational field strength, g, as the force per unit
charge on a small positive test charge placed at the mass on a small test mass placed at the point,
point,
Recall and use the inverse square law for the force two electric charges in the form
between
QQ
1
(Coulomb's Law)
F  k 1 2 2 where k 
4
r
two masses in the form
F k
m1m2
where k = G (Newton's Law of
r2
Gravitation)
Recall that
F can be attractive or repulsive
Recall and use …
E
1
Q
for the field strength due to a point
40 r 2
F is attractive only
g
Gm
for the field strength due to a point mass
r2
charge in free space or air
Recall and use the equations….
•
•
•
•
•
a point charge in terms of the work done in a point mass in terms of the work done in bringing
bringing unit positive charge from infinity to that a unit mass from infinity to that point,
point,
VE 
1 Q
40 r
Vg 
 GM
r
Know that the change in potential energy a point charge moving in any electric field
of …
 qVE ,
Use these relationships.
a point mass moving in any gravitational field
Recall that the field strength at a point is E = - slope of the VE – r graph at that point
given by …
Use these relationships.
g = - slope of the Vg– r graph at that point, and for
uniform fields.
Know that the potential difference is given the area under the E – r graph.
by …
the area under the g – r graph.
 mV g
44
Define potential at a point due to …
PH4.5 APPLICATION TO ORBITS IN THE SOLAR SYSTEM AND
THE WIDER UNIVERSE
Content







Kepler's Laws of Planetary Motion
Circular orbits of satellites, planets and stars
Centre of Mass
Missing mass in galaxies – Dark Matter
Objects in mutual orbit
Doppler shift of spectral lines
Extra-solar planets
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
state Kepler's three Laws of Planetary Motion,
(b)
recall and use Newton's law of Gravitation F  G
m1m2
in
r2
simple examples, including the motion of planets and
satellites;
(c)
derive Kepler's 3rd Law, for the case of a circular orbit from
Newton's Law of Gravity and the formula for centripetal
acceleration,
(d)
use data on orbital motion, such as period or orbital speed, to
calculate the mass of the central object;
(e)
appreciate that the orbital speeds of objects in spiral galaxies
implies the existence of dark matter;
(f)
calculate the position of the centre of mass of two
spherically-symmetric objects, given their masses and
separation, and calculate their mutual orbital period in the
case of circular orbits,
(g)
use the Doppler relationship in the form
(h)
calculate a star's radial velocity (i.e. the component of its
velocity along the line joining it and an observer on the
Earth) from data about the Doppler shift of spectral lines,
(i)
use data on the variation of the radial velocities of the bodies
in a double system (e.g. a star and orbiting planet) and their
orbital period to determine the masses of the bodies for the
case of a circular orbit edge on as viewed from the Earth



v
c
;
45
PH5 Assessment Unit – MAGNETISM, NUCLEI & OPTIONS
Advanced Level A2
The Unit is built around a core relating to the following Subject Criteria content:
3.4 (e)
3.7 (c) – (d)
3.8 (b) – (c)
Electrical circuits: capacitance
Nuclear Physics: nuclear decay, nuclear energy
Fields: B-fields, flux and electromagnetic induction
SPECIFICATION
PH5.1 CAPACITANCE
Content
•
•
•
•
•
•
The parallel plate capacitor.
Concept of capacitance.
Factors affecting capacitance.
Energy stored in a capacitor.
Capacitors in series and parallel.
Capacitor discharge.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
understand that a simple parallel plate capacitor consists of a
pair of equal parallel metal plates separated by vacuum or air,
(b)
understand that the capacitor stores energy by transferring
charge from one plate to the other, so that the plates carry
equal but opposite charges (the net charge being zero),
(c)
define capacitance as C 
(d)
use C 
(e)
know that a dielectric increases the capacitance of a vacuumspaced capacitor;
(f)
recall that the E field within a parallel plate capacitor is
uniform and of value V/d,
(g)
use the equation U  12 QV for the energy stored in a
capacitor,
(h)
use formulae for capacitors in series and in parallel,
(i)
understand the process by which a capacitor discharges
through a resistor,
(j)
use the equation
o A
d
Q
,
V
for a parallel plate capacitor, with no dielectric,
Q  Q0 e  RC where RC is the time constant.
t
46
PH5.2 B-FIELDS
Content
•
•
•
•
•
•
•
•
•
Concept of magnetic fields (B-fields).
Force on a current-carrying conductor.
Force on a moving charge.
Magnetic fields due to currents.
Effect of a ferrous core.
Force between current – carrying conductors.
Definition of the ampere.
Measurement of magnetic field strength B.
Deflection of beams of charged particles in electric and
magnetic fields.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
predict the direction of the force on a current-carrying
conductor in a magnetic field,
(b)
define magnetic field B by considering the force on a currentcarrying conductor in a magnetic field; recall and use
F = BIl sin  ,
(c)
use F  Bqv sin  for a moving charge in a magnetic field;
(e)
understand the processes involved in the production of a Hall
voltage and understand that VH  B for constant I.
(f)
describe how to investigate steady magnetic fields with a
Hall probe,
(g)
sketch the magnetic fields due to a current in
(i)
(ii)
(h)
a long straight wire,
a long solenoid,
use the equations B 
 I
and B    nI for the field
2a
strengths due to a long straight wire and in a long solenoid,
(i)
know that adding an iron core increases the field strength of a
solenoid,
(j)
explain why current-carrying conductors exert a force on
each other and predict the directions of the forces,
(k)
understand how the equation for the force between two
currents in straight wires leads to the definition of the
ampere,
(m)
describe quantitatively how ion beams, i.e. charged particles,
are deflected in uniform electric and magnetic fields,
47
(o)
48
apply knowledge of the motion of charged particles in
magnetic and electric fields to linear accelerators, cyclotrons
and synchrotrons.
PH5.3 ELECTROMAGNETIC INDUCTION
Content
•
•
•
•
Magnetic flux.
Laws of electromagnetic induction.
Calculation of induced emf.
Self induction.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall and define magnetic flux as   AB cos  and flux
linkage = N
/
(b)
recall the laws of Faraday and Lenz,
(c)
recall and use e.m.f. = – rate of change of flux linkage and
use this relationship to derive an equation for the e.m.f.
induced in a linear conductor moving at right angles to a
uniform magnetic field,
(e)
relate qualitatively the instantaneous e.m.f. induced in a coil
rotating at right angles to a magnetic field to the position of
the coil, flux density, coil area and angular velocity;
(f)
understand and use the terms frequency, period, peak value
and root-mean-square value when applied to alternating
voltages and currents,
(g)
understand that the r.m.s. value is related to the energy
V
dissipated per cycle, and use the relationships Vr.m.s.  0
2
I
and I r.m.s  0
2
(h)
recall that the mean power dissipated in a resistor is given by
V2
P  VI 
 I 2 R , where V and I are the r.m.s. values;
R
(i)
describe the use of a cathode ray oscilloscope to
measure:
(ii)
a.c. and d.c. voltages and currents,
(iii)
frequencies.
49
PH5.4 RADIOACTIVITY AND RADIOISOTOPES
Content
•
•
•
•
Radioactive decay.
Half-life.
Applications of radioactivity.
Hazards and safety precautions.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
recall the spontaneous nature of nuclear decay; describe the
nature of ,  and  radiation, and use equations to represent
the nuclear transformations using the ZA X notation,
(b)
describe methods used to distinguish between ,  and 
radiation and explain the connections between the nature,
penetration and range for ionising particles,
(c)
account for the existence of background radiation and make
allowance for this in experimental measurements,
(d)
explain what is meant by half-life T1 ,
2
(e)
define activity A and the becquerel,
(f)
define decay constant ( λ ) and recall and use the equation A
= –  N.
(g)
recall and use the exponential law of decay in graphical and
algebraic form,
[ N  N o e t ( or N 
No
A
) and A  Ao e t ( or A  xo )
x
2
2
where x is the number of half-lives elapsed – not necessarily
an integer,]
50
log e 2
,
T 12
(h)
derive and recall that  
(i)
describe briefly the use of radioisotopes (any two
applications),
(j)
show an awareness of the biological hazards of ionising
radiation e.g. whether exposed to external radiation or when
radioactive materials are absorbed (ingestion and/or
inhalation).
PH5.5 NUCLEAR ENERGY
Content
•
•
•
Binding Energy.
Fission and Fusion.
Nuclear Reactors.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
appreciate the association between mass and energy and
recall that E  mc 2 ,
(b)
calculate the binding energy for a nucleus and hence the
binding energy per nucleon, making use, where necessary, of
the unified atomic mass unit (u) and the electron-volt (eV),
(c)
apply the conservation of mass/energy to particle interactions
– e.g. fission, fusion and neutrino detection interactions
(d)
describe the relevance of binding energy per nucleon to
nuclear fission and fusion,
(e)
explain how neutron emission gives the possibility of a chain
reaction,
(f)
understand and describe induced fission by thermal neutrons
and the roles of moderator, control rods and coolants in
thermal reactors,
(g)
understand and recall the factors influencing choice of
materials for moderator, control rods and coolant,
(i)
discuss the environmental problems posed by the disposal of
the waste products of nuclear reactors.
51
OPTIONAL CONTENT IN UNIT A2
The following section contains the 5 optional sections to A2. It is anticipated that candidates
will study only one of these optional topics. The approximate teaching time required for each
option is 15 hours. The questions on the optional topics will occupy a separate section in the
PH5 paper and account for 20 marks.
Option A2/A
Further Electromagnetism and Alternating Currents
Content

Mutual induction.

Simple treatment of the transformer.

Self induction and self inductance

A.C. behaviour of a capacitor and an inductor; reactance,
mean power.

Vector treatment of RC, RL and RCL series circuits;
impedance.

Uses: simple RC filters, tuned circuits.
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
describe, in terms of electromagnetic induction, how a
changing current in one coil induces an e.m.f. in another coil;
(b)
understand that a closed-loop iron core enables a real
transformer to approximate to the ideal case where there is
no flux leakage;
(c)
understand and recall that that if there is no flux leakage, or
V
N
voltage drops in the primary or secondary, then 1  1 ;
V2 N 2
(d)
understand and recall that if there were no energy dissipation
in the transformer itself, then V1 I1  V2 I 2 , in which the p.d.s
and currents are r.m.s. values;
(e)
recall that in practice there is some energy dissipation due to
(i)
(ii)
(iii)
(f)
recall that these losses can be reduced by
(i)
(ii)
(iii)
(g)
52
the resistance of the primary and secondary coils,
eddy currents in the iron core,
energy used cyclically to change the magnetisation
of the core;
using thick enough wires for the coils,
laminating the core,
choosing a suitable alloy for the core;
describe, in terms of electromagnetic induction, how a
changing current in a coil induces in that coil an e.m.f.,
whose direction is such as to oppose the change in current;
(h)
define the self-inductance of a coil by the equation
I
E  L
;
t
(i)
understand the 90° phase lag of current behind p.d. for an
inductor in a sinusoidal a..c. circuit;
(j)
recall that
Vrms
I rms
is called the reactance, X L , of the inductor,
and use the equation X L   L ;
(k)
understand the 90° phase lead of current ahead of p.d. for a
capacitor in a sinusoidal a..c. circuit, and use the
1
equation X C 
;
C
(l)
recall that the mean power dissipation in an inductor or a
capacitor is zero;
(m)
add p.d.s across series RC, RL and RCL combinations using
phasors;
(n)
calculate phase angle and impedance, Z, (defined as
Vrms
I rms
) for
such circuits;
(o)
derive an expression for the resonance frequency of an RCL
series circuit;
(p)
understand that the sharpness of the resonance curve is
L
determined by the ratio
, known as the Q factor of the
R
circuit;
(q)
understand how a series LCR circuit can be used to select
frequencies;
(r)
understand how a CR circuit can be used as a simple highpass or low-pass filter;
53
Option A2/B
Revolutions in Physics
This option module consists of two topics.
Topics

The Newtonian Revolution

Electromagnetism and Space-Time
AMPLIFICATION OF CONTENT
1. The Newtonian Revolution
General Approach
•
Why do things move in the way they do? How our concepts of force
and motion developed during the seventeenth century, culminating
with Newton's Principia.
•
The course is structured around the study of some 10 short extracts
from the (translated) works of the giants of the revolution, including
Kepler, Descartes and Galileo, as well as Newton himself.
•
Questions about the nature of science will arise and invite discussion
e.g. can an abstract mathematical law really be said to explain what
makes the planets move in ellipses?
•
WJEC will provide teachers' notes, including guidance on what to
look for in the extracts.
•
In examinations, candidates would be expected to recognise, say, a
diagram from Newton or Descartes, or a paragraph from Galileo and
to comment on its significance. This wouldn't, of course, be the only
sort of question.
Ground to be Covered
54
•
The official (post-Aristotle) view of the 'perfect', eternal, circular
motion of heavenly bodies and the short-lived motion of bodies (like
carts and arrows) on the Earth.
•
Ptolemy's earth-centred universe and Copernicus's Sun-centred
system
•
Kepler's elliptical orbits.
•
Galileo: the Law of Inertia and the heliocentric system made
plausible.
•
Descartes: A mechanistic universe of particles and contact forces,
including the vortex theory of the solar system. No place for occult
forces and influences in Descartes' world?
•
Newton's 'shoulders of giants' synthesis: the link between force and
motion, how a central force can account for planetary motion, the
inverse square law, celestial and terrestrial dynamics unified…
•
Questions raised: Did Newton really explain anything? Was Newton
satisfied with his own work? What were the effects of the Newtonian
revolution on the way people thought? Has Newton's work been
superseded? …
2. Electromagnetism and Space-Time
General Approach
•
This course sketches how the evidence was uncovered for
light being an electromagnetic wave, and how this preceded
revolutionary changes in our views of time and space.
•
The study of some eight shortish extracts from the works of
Young, Faraday, Maxwell, Hertz and others will help to give
the course structure. In examinations, candidates would be
expected to recognise a diagram or a paragraph from these
extracts and to comment on its significance.
•
Questions about the nature of science will arise and invite
discussion e.g. Can science and common sense be at odds?
•
WJEC will provide teachers' notes, including guidance on
what to look for in the extracts.
Ground to be Covered
•
The background: exciting work in Physics around 1800:
Young's resurrection of the wave theory of light, Galvani's
twitching frog's leg and Volta's pile.
•
Oersted's discovery that an electric current gives rise to a
magnetic field and Ampère's quantitative work.
•
Faraday's lines of force, tending to contract along their length
and to expand sideways, explaining the forces of coils or
magnets (or charges) on one another – contrasted with the
'action at a distance' theories of Ampère and others.
•
Faraday's discovery of electromagnetic induction.
•
Maxwell's espousal of Faraday's lines of force as physical
things and a glimpse of his early 'vortex' model, which led to
his prediction of electromagnetic waves with the same speed
as light – surely not a co-incidence.
•
Maxwell's realisation that the testable Physics in his model
could all be summed up in four [sets of] equations, so the
model itself could be ditched.
•
Hertz: Maxwell vindicated.
•
The aether: a medium needed for the propagation of light and
other e-m waves? The purpose and principle and result of the
Michelson-Morley experiment.
•
Einstein's Special Relativity accounts naturally for this result.
A simple thought experiment on time dilation to give a
flavour of the theory.
55
Option A2/C
Materials
Content

Hooke's Law

Stress-strain and the Young Modulus

Strain energy – elastic hysteresis

Elastic and plastic behaviour

Composite materials
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
Classify solids as crystalline, amorphous and polymeric in
terms of their microscopic structure.
(b)
Describe an experiment to investigate the behaviour of a
spring in terms of load and extension, recall and use Hooke's
law and define the spring constant as force per unit
extension. F  k x
(c)
F
Define tensile stress     and tensile strain

A
   l  and the Young modulus and perform simple


l 

calculations; compare the Young modulus of various solids
56
(d)
Describe an experiment to determine the Young modulus of a
metal in the form of a wire.
(e)
Deduce the strain energy in a deformed solid material from
the area under a force/extension graph  12 F x  and recall
and derive the equation: strain energy per unit volume
 12  and apply to cases in which K.E is absorbed by a wire
or rope.
(f)
Describe the main features of force/extension, stress/strain
graphs for ductile materials such as copper and compare
these with less ductile metals such as steel.
(g)
Describe the deformation of ductile materials at the
molecular level and distinguish between elastic and plastic
strain.
(h)
Describe, at the molecular level, the effect of dislocations
and the strengthening and stiffening of materials by the
introduction of dislocation barriers such as foreign atoms,
other dislocations and grain boundaries;
(i)
understand, on a simple molecular level, how superalloys
have been developed to withstand extreme conditions, and
describe some of their uses;
(j)
Describe in molecular terms failure mechanisms in ductile
materials: ductile fracture (necking), creep and fatigue.
(k)
Understand that heat treatment processes may control the
mechanical properties of metals: cold working (work
hardening), annealing (e.g. copper) and quench hardening
(e.g. steel)
(l)
Demonstrate an understanding of the force/extension,
stress/strain graph for a brittle substance such as glass and be
able to compare it with the graph for a ductile material.
(m)
Describe brittle fracture in molecular terms and the effect of
surface imperfections on breaking stress (UTS) and the
increased breaking stress of thin glass fibres.
(n)
Describe thermoplastic (e.g. polythene) and thermosetting
(e.g. melamine) polymers at the molecular level. Compare
and contrast their properties and describe some of their uses.
(o)
Demonstrate an understanding of the force/extension,
stress/strain graph for polymeric substances (rubber and
polyethylene).
(p)
Compare the behaviour of rubber and polyethylene in terms
of molecular structure and behaviour under stress with
reference also to the effect of temperature. Understand the
importance of hysteresis in rubber.
(q)
Recall that materials do not always behave in a similar way
in tension and compression and that crack propagation is
more difficult under compression- with particular reference
to concrete and prestressed glass as examples.
(r)
Understand that composite materials are developed to take
advantage of the mechanical properties of the individual
materials from which they are made, with reference to
vehicle tyres, reinforced concrete, fibre reinforced polymers
(e.g. glass and carbon) and wood based composites used as
examples.
57
Option A2/D
Biological Measurement and Medical Imaging
Content

X-rays

Ultrasound

Magnetic resonance imaging

Nuclear imaging
AMPLIFICATION OF CONTENT
Candidates should be able to:
(a)
describe the nature and properties of X-rays.
(b)
describe the production of X-ray spectra including methods
of controlling the beam intensity, photon energy, image
sharpness, contrast and patient dosage.
(c)
describe the use of high energy X-rays in the treatment of
patients (therapy) and low energy X-rays in diagnosis.
(d)
use the equation I  I 0 exp    x  for the attenuation of Xrays;
(e)
understand the use of X-rays to give images of internal
structures, image intensifiers and contrast media.
(f)
describe the use of a rotating beam CT scanner
(computerised axial tomography).
(g)
describe the generation and detection of Ultrasound using
piezoelectric transducers;
(h)
describe scanning with Ultrasound for diagnosis including Ascans and B-scans (use of real time B-scans is not required)
incorporating
examples and applications;
(i)
understand the significance of acoustic impedance, defined
by Z  c  for the reflection and transmission of sound
waves at tissue boundaries, including appreciating the need
for a coupling medium;
(j)
understand the use of the Doppler equation



v
c
to study
blood flow using an ultrasound probe.
58
(k)
understand the principles of magnetic resonance with
reference to precession nuclei, resonance and relaxation time.
(l)
describe the use of the MRI in obtaining diagnostic
information about internal structures.
(m)
discuss the advantages and disadvantages of ultra sound
imaging, X-ray imaging and MRI in examining internal
structures;
(n)
understand the structure of the heart as a double pump
(o)
describe methods of detecting electrical signals at the skin
surface.
(p)
describe the basic method of operation of an ECG machine,
and explain the characteristic waveform by considering the
heart's response to a potential originating at the sino-atrial
node;
(q)
describe the effects of α, β, and γ radiation on living matter.
(r)
define and use the Gray (Gy) as the unit of absorbed dose
and the sievert (Sv) as the unit of dose equivalent
(s)
describe uses of radionuclides as tracers to image body parts
with particular reference to I-123 and I-131.
(t)
describe the use of the gamma camera including the
principles of the collimator, scintillation counter and
photomultiplier.
(u)
understand the principles of positron emission tomography
(PET) scanning and its use in detecting tumours.
59
Option A2/E
ENERGY MATTERS
This Option addresses energy in the real world. While the main emphasis is on the physics of
energy producing and conserving processes, candidates should have an awareness of current
energy issues (economic, environmental, humanitarian and political) together with an
overview of key statistics and trends. A typical examination question might consist of a
topical passage of from which students will draw conclusions, extract data for calculations
etc. Much of the underlying physics is straightforward and will have been treated earlier in the
specification as indicated below:
PH1.3 Energy concepts
PH1.5 Resistance
PH2.1 Waves
PH2.3 Photons
PH2.5 Matter forces and the universe (a) to (d)
PH4.3 Thermal physics
PH5.5 Nuclear energy.
Content

Renewable energy sources

Energy storage

Nuclear, fossil and other non-renewable energy sources

Hazards and harmful consequences

Mass transfer processes

Energy transfer processes

Work from heat
AMPLIFICATION OF CONTENT
Candidates should be able to:
60
(a)
estimate hydroelectric, tidal and wind power from simple
mechanical models;
(b)
be aware of existing and intended projects: hydroelectric
(e.g. Yangtze); tidal (e.g. La Rance, Severn); wind (e.g.
London Array);
(c)
understand the principle of energy storage in projects such as
Ffestiniog and Dinorwig;
(d)
interpret equations representing fission and fusion reactions,
and calculate resulting energies from given mass data;
(e)
understand the principles underlying breeding and
enrichment in nuclear fission applications;
(f)
show an understanding of the difficulties in producing
sustained fusion power and be aware of current progress
(JET) and prospects (ITER);
(g)
recognise convection as mass movement of fluids and
understand that energy losses by convection can be
minimised by, for example, trapping gas in bubbles;
(h)
understand and apply the thermal conduction equation in the
Q

  AK
form
(derivation and recall not required);
t
x
(i)
be aware of the origin and means of transmission of solar
energy, and the form of the sun’s power spectrum;
(j)
recall and use the Stefan-Boltzman T4 law and the Wien
displacement law;
(k)
understand what is meant by, and calculate, the Solar
Constant from the sun’s temperature and geometrical
formulae in the maths datasheet;
(l)
be aware of the problems in harnessing solar energy and the
limitations of solar cells;
(m)
recognise the environmental effects of carbon fuels and
understand the basis of the greenhouse effect;
(n)
understand the principles of fuel cell operation and
appreciate the benefits of fuel cells particularly regarding
greenhouse gas emission;
(o)
understand the principles underlying the ideal heat engine,
the Carnot cycle, refrigerators and heat pumps (including
recent applications e.g. the Cardiff Senedd);
(p)
state and explain the second law of thermodynamics (Kelvin
form); understand how the second law places an upper limit
on the efficiencies of heat engines, for example of the
turbines in conventional and nuclear power stations.
61
PH6 Internal Assessment Unit – Experimental Physics
This unit gives candidates the opportunity of demonstrating their ability to
carry out their own investigations and to analyse and evaluate secondary
experimental data. The unit is entirely synoptic in character.
AMPLIFICATION OF CONTENT
Candidates should be able to:
•
•
•
plan and carry out an investigation at a level appropriate to
the A2 course;
analyse and evaluate data from their own investigation and
from secondary sources using graphical and mathematical
techniques including those specific to the A2 course;
combine uncertainties arising from various measurements
and judge which uncertainties are the most significant in a
procedure;
Task Details
Candidates are required to undertake individually, under controlled
conditions, two tasks: Task A and Task B. The tasks are devised by the
WJEC, undertaken under controlled conditions and the outcomes assessed by
the centre using marking schemes provided by the WJEC.
Task A: Data Analysis
This is a 45 minute task, carrying 25 marks. Candidates are provided with a
set of experimental data on a topic drawn from the A level specification. They
are given details of how the data were obtained. They will be expected to:



analyse the data graphically and algebraically in order to establish a
relationship between the variables and/or to derive a significant
quantity – the graphical and analytic techniques may involve log-log
or semi-log plots and the use of powers (positive or negative);
derive an uncertainty from the graphical and/or algebraic analysis and
express the solution in SI units to a precision commensurate with the
uncertainty;
make appropriate comments upon the analysis.
Task B: Investigation
This is a 75 minute task, carrying 25 marks. Candidates are provided with a
set of apparatus and an experimental problem. They will be expected to:


plan the safe use of some or all of the apparatus to investigate the
problem (15 minutes);
carry out their planned investigation, including analysing their data,
drawing conclusions and evaluating both the data and the
experimental techniques (1 hour).
In order to make the task discriminating and also to allow all candidates to
make progress, provision is made for the supervisor to provide extra
information where necessary. The provision of such information will result in
marking penalties.
Both tasks will be carried out in the second half of the spring term. The
details for the timing of the tasks and the receipt of the appropriate
62
information will be given in the WJEC booklet Manual of Internal
Assessment which is produced annually.
The candidates’ work is marked by the supervisor. The results are be
forwarded to the WJEC and the candidates’ work presented for moderation in
line with the procedures of the WJEC.
63
5
SCHEME OF ASSESSMENT
Synoptic Assessment
Synoptic assessment, testing candidates' understanding of the connections between
the different elements of the subject and their holistic understanding of the subject, is
a requirement of all A level specifications. In the context of Physics this means:
PH4: The work on vibrations, thermodynamics, electric and gravitation fields and
potentials and the Doppler shift of spectral lines, builds upon concepts built up in the
AS course. Questions examine these synoptic aspects.
PH5: All compulsory areas of this unit draw upon work in previous units: e.g.
capacitors on electrical circuits (PH1) and electric fields (PH4); motion of charges in
magnetic fields on circular motion (PH4); nuclear properties on particles (PH2).
Questions are set which link these themes. The Case Study (section B) is synoptic in
nature.
PH6: All aspects of the two parts of this internally-assessed unit are synoptic in
nature.
Quality of Written Communication
Candidates will be required to demonstrate their competence in written
communication in all assessment units where they are required to produce extended
written material: PH2, PH5 and PH6. Mark schemes for these units include the
following specific criteria for the assessment of written communication.
 legibility of text; accuracy of spelling, punctuation and grammar; clarity of
meaning;
 selection of a form and style of writing appropriate to purpose and to complexity
of subject matter;
 organisation of information clearly and coherently; use of specialist vocabulary
where appropriate.
The front pages of all the external assessment papers include an emboldened
statement informing candidates of the necessity for expressing themselves clearly
using correct technical terms. The marking schemes covers include a statement of the
requirement to take level of language into account and the detailed marking key
indicates, using (QWC) places where the quality of the written communication will
contribute to the assessment f performance.
64
Awarding, Reporting and Re-sitting
The overall grades for the GCE AS qualification will be recorded as a grade on a
scale from A to E. The overall grades for the GCE A level qualification will be
recorded on a grade scale from A* to E. Results not attaining the minimum standard
for the award of a grade will be reported as U (Unclassified). Individual unit results
and the overall subject award will be expressed as a uniform mark on a scale common
to all GCE qualifications (see table below). The grade equivalence will be reported as
a lower case letter ((a) to (e)) on results slips, but not on certificates:
Max.
UMS
A
B
C
D
E
PH1 & PH2
(weighting 20%)
PH3 & PH6
(weighting 10%)
PH4
(weighting 18%)
PH5
(weighting 22%)
120
96
84
72
60
48
60
48
42
36
30
24
108
86
76
65
54
43
132
106
92
79
66
53
AS Qualification
300
240
210
180
150
120
A Qualification
600
480
420
360
300
240
At A level, Grade A* will be awarded to candidates who have achieved a Grade A in
the overall A level qualification and an A* on the aggregate of their A2 units.
Candidates may re-sit units prior to certification for the qualification, with the
best of the results achieved contributing to the qualification. Individual unit
results, prior to certification of the qualification have a shelf-life limited only
by the shelf-life of the specification.
65
Glossary
Item
Definition
Activity A.
Becquerel Bq.
The rate of decay (number of disintegrations per second) of a
sample of radioactive nuclei.
Unit: Bq=s-1.
Ampere A.
The ampere is that constant current which when flowing
through two infinite, thin, parallel wires, one metre apart in
vacuum, produces a force between the wires of 210-7N per
metre of length. Unit: A.
Amplitude
The amplitude is defined as the maximum displacement of
any particle from its equilibrium position.
Amplitude A of an
oscillating object
The maximum value of the object’s displacement (from its
equilibrium position).
Angular velocity ω.
For a point describing a circle at uniform speed, the angular
velocity ω is equal to the angle θ swept out by the radius in
time t divided by t . (ω= θ/t)
UNIT: [rad] s-1
Atomic mass
number, A
The atomic mass number of an atom is the number of
nucleons (number of protons + number of neutrons) in its
nucleus.
Atomic number, Z.
The atomic number of an atom is the number of protons in its
nucleus. [This determines the chemical element which the
atom represents.]
Avogdadro constant
N A.
This is the number of particles in a mole. (NA=6.021023 to 3
figs).
Binding energy of a
nucleus.
The energy that has to be supplied in order to dissociate a
nucleus into its constituent nucleons. [It is therefore not
energy which a nucleus possesses.] Unit: J [or MeV]
Boyle’s law
For a fixed mass of gas at constant temperature, the pressure
varies inversely as the volume. (p = k/V)
Capacitor, reactance
of.
When an AC voltage is applied to a capacitor, the reactance is
given by XC = Vrms/Irms where Vrms and Irms are, respectively,
the voltage across and the current ‘through’ the capacitor.
It is equal to 1/C (or 1/2fC).
Capacitor.
A pair of parallel metal plates, a small distance apart,
insulated from one another.
Centre of gravity.
The centre of gravity is the single point within a body at
which the entire weight of the body is considered to act.
Coherence
Waves or wave sources, which have a constant phase
difference between them (and therefore must have the same
frequency) are said to be coherent.
Conservation of
Energy cannot be created or destroyed, only transformed from
energy (principle of). one form to another.
66
Item
Damping.
De Broglie
relationship λ = h/p
Decay constant λ.
Definition
Damping is the dying away of amplitude with time of free
oscillations due to resistive forces.
The key relationship relating to wave-particle duality. It gives
the wavelength λ associated with a moving particle in terms of
its linear momentum p and the Planck constant h.
The constant which appears in the exponential decay law
N  N 0 e  t and determines the rate of decay (the greater λ is,
the more rapid the rate of decay). It is related to half life by λ
= ln2/ T1 .
2
Unit:
Displacement
e.m.f.
s-1
The displacement of a point B from a point A is the shortest
distance from A to B, together with the direction. UNIT: m.
The e.m.f. of a source is the energy converted from some
other form (e.g. chemical) to electrical potential energy per
coulomb of charge flowing through the source. Unit: volt (V)
[= JC-1].
Efficiency
% Efficiency = 100(Useful energy obtained)/(Total energy
input).
Elastic collision.
A collision in which there is no loss of kinetic energy.
This is the rate of flow of electric charge. I = ∆Q/∆t.
Electric current, I.
Unit: A
Electric field
strength E.
The force experienced per unit charge by a small positive
charge placed in the field. Unit: Vm-1.
Electric potential VE.
Electric potential at a point is the work done per unit charge in
bringing a positive charge from infinity to that point. Unit: V.
[= JC-1]
Electrical
Resistance, R.
The resistance of a conductor is the p.d. (V) placed across it
divided by the resulting current (I) through it. R = V / I
Unit: ohm () [= VA-1].
Electron volt (eV).
This is the energy transferred when an electron moves
between two points with a potential difference of 1 volt
between them. 1 eV = 1.6  10-19 J
[Within the context of particle accelerators it can also be
defined as: the energy acquired by an electron when
accelerated through a pd of 1V.]
Electron volt. (eV)
This is the energy transferred when an electron moves
between two points with a potential difference of 1 volt
between them. 1 eV = 1.6  10-19 J
67
Item
Energy
The energy of a body or system is the amount of work it can
do. UNIT: joule (J).
Faraday’s law
When the flux linking an electrical circuit is changing, an emf
is induced in the circuit of magnitude equal to the rate of
change of flux.
Flux linkage NФ.
If the above coil consists of N turns, the flux linkage is given
by NФ. Unit: Wb or Wb turn.
Forced oscillations.
These occur when a sinusoidally varying force is applied to an
oscillatory system, causing the system to oscillate with the
frequency of the applied force.
Free oscillations.
Free oscillations occur when an oscillatory system (such as a
mass on a spring, or a pendulum) is displaced and released.
[The frequency of the free oscillations is known as the
natural frequency.]
Frequency f.
The number of circuits or cycles per second.
Frequency of a wave
The frequency of a wave is the number of cycles of a wave
that pass a given point in one second,
or equivalently
The frequency of a wave is the number of cycles of oscillation
performed by any particle in the medium through which the
wave is passing.
Gravitational field
strength g.
The force experienced per unit mass by a mass placed in the
field. Unit: ms-2 or Nkg-1.
Gravitational
potential Vg.
Gravitational potential at a point is the work done per unit
mass in bringing a mass from infinity to that point.
Unit: Jkg-1.
Half life T1
The time taken for the number of radioactive nuclei N (or the
activity A) to reduce to one half of the initial value. Unit: s.
2
68
Definition
Hooke’s Law
The tension in a spring or wire is proportional to its extension
from its natural length, provided the extension is not too great.
Hooke’s Law.
The extension of an elastic object such as a wire or spring is
proportional to the stretching force, provided the extension is
not too large.
(F = kx).
Ideal gas.
An ideal gas strictly obeys the equation of state
pV = nRT.
Inductor, reactance
of.
When an AC voltage is applied to an inductor, the reactance is
given by XL = Vrms/Irms where Vrms and Irms are, respectively,
the voltage across and the current through the inductor.
It is equal to L (or 2fL)
Inelastic collision.
A collision in which kinetic energy is lost.
Item
Definition
Instantaneous
Acceleration
The instantaneous acceleration of a body is its rate of change
of velocity. UNIT: ms-2
Instantaneous Speed
instantaneous speed = rate of change of distance
UNIT: ms-1.
Instantaneous
Velocity
The velocity of a body is the rate of change of displacement.
UNIT: ms-1
Intensity of a wave
Energy per second passing normally through a given area
Area
Internal energy
The internal energy (of say a container of gas) is the sum of
the potential and kinetic energies of the molecules.
Ionisation
The removal of one or more electrons from an atom.
Ionisation energy
The ionization energy of an atom is the minimum energy
needed to remove an electron from the atom. Unit: J
Isotope.
Isotopes are atoms with the same number of protons, but
different numbers of neutrons in their nuclei.
Lenz’s Law.
The direction of any current resulting from an induced emf is
such as to oppose the change in flux linkage that is causing
the current.
Longitudinal wave
A longitudinal wave is one where the particle oscillations are
in line with (parallel to) the direction of travel (or
propagation) of the wave.
Magnetic flux
density B.
A length l of wire perpendicular to a magnetic flux density B,
carrying a current I, experiences a force of magnitude BIl.
Unit: T (Tesla) [= NA-1m-1]
Magnetic flux Ф.
Weber Wb.
If a single-turn coil of wire encloses an area A, and a magnetic
field B makes an angle θ with the normal to the plane of the
coil, the magnetic flux through the coil is given by Ф = AB
cos θ. Unit: Wb=Tm2.
Mean Acceleration
Mean Acceleration =
change in velocity v

time taken
t
UNIT: ms-2.
Mean Speed
Mean speed =
total distance travelled x

total time taken
t
UNIT: ms-1.
Mean Velocity
Mean velocity =
total displacement
total time taken
UNIT: ms-1.
Mole.
This is the amount of substance that has the same number of
particles (usually atoms or molecules), as there are atoms in
exactly twelve grammes of the nuclide 12 C .
69
Item
70
Definition
Momentum
The momentum of an object is its mass multiplied by its
velocity. (p = mv). It is a vector.
UNIT: kg m s-1
Newton’s law of
gravitation.
The gravitational force between two objects is directly
proportional to the product of their masses and inversely
proportional to the distance between their centres. F =
Gm1m2/r2
Newton’s Laws of
Motion. 1st Law
An object continues in a state of uniform motion in a straight
line, or remains at rest, unless acted upon by a resultant force.
Newton’s Laws of
Motion. 2nd Law
The rate of change of momentum of an object is proportional
to the resultant force acting on it, and takes place in the
direction of that force.
Newton’s Laws of
Motion. 3rd Law
If an object A exerts a force on a second object B, then B must
exert a force which is equal in magnitude but opposite in
direction on A.
A
Z
X is the chemical symbol of the element, A the mass number
(number of protons plus number of neutrons) and Z the atomic
number (number of protons).
X notation
Nucleon.
Protons and neutrons have similar masses. They are both
classed as ‘nucleons’.
Nuclide
A nuclide is a particular variety of nucleus, that is a nucleus
with a particular A and Z.
Ohm’s Law.
The current flowing through a metal wire at constant
temperature is proportional to the p.d. across it.
Period T for a point
describing a circle.
Time taken for one complete circuit.
Period T for an
oscillating body
Time taken for one complete cycle.
Phase difference
Phase difference is the difference in position of 2 points
within a cycle of oscillation measured as a fraction of the
cycle. [Alternatively it can be expressed as an angle where
one whole cycle is 360]
Photoelectric effect
When light or ultraviolet radiation of short enough
wavelength falls on a surface, electrons are emitted from the
surface. This is the photoelectric effect.
Potential difference
(p.d.), V.
The p.d. between two points is the energy converted from
electrical potential energy to some other form per coulomb of
charge flowing from one point to the other.
Unit: volt (V) [= JC-1].
Potential energy.
This is energy possessed by virtue of position. (e.g.
Gravitational PE = mgh)
Item
Definition
Power
This is the work done per second, or energy converted or
transferred per second.
UNIT: watt (W) [= Js-1].
Radioisotopes
Isotopes (of the same element) have the same atomic number
Z but different mass number A. Radioisotopes are simply
isotopes which are radioactive.
Relative
permeability μr.
When magnetic material of relative permeability μr fills a long
solenoid, the magnetic flux density in the material is given by
B = μrB0 where B0 is the flux density when the solenoid is
evacuated.
Relative permittivity
εr.of an insulator or
‘dielectric’
If capacitance is measured first with vacuum between the
plates and then with a slab of insulator between, the
capacitance increases by a factor εr
Resistivity, 
The resistance, R, of a metal wire of length L and crosssectional area A is given by R =  L / A, in which the
resistivity, is a constant (at constant temperature) for the
material of the wire.
Unit: ohm-metre (m)
Resonance.
If, in forced vibrations, the frequency of the applied force is
equal to the natural frequency of the system (e.g. mass on
spring), the amplitude of the resulting oscillations is very
large. This is resonance.
This is a form of average, which is really self defined. Thus
for three discrete quantities 1,2 and 3, the r.m.s value is given
Root mean square
value (r.m.s.).
by 12  2 2  3 2  / 3  2.16 . For sinusoidal variations the
r.m.s. value over a complete cycle is given by the peak
(maximum) value divided by 2 .
(e.g. Irms =IO/ 2 )
Scalar
A scalar is a quantity that has magnitude only.
Self inductance L.
Henry H
When a current I through a coil produces a flux linkage NФ,
the self inductance of the coil is given by L= NФ/I.
Unit: H=WbA-1=Tm2A-1 [= VsA-1]
Simple harmonic
motion (shm).
Shm occurs when an object moves such that its acceleration is
always directed toward a fixed point and proportional to its
distance from the fixed point. (a=-ω2x)
Simple harmonic
motion (shm).
(Alternative
definition).
If the displacement x of a point changes with time t according
to the equation x = a sin(ωt+ε) where a, ω and ε are
constants, the motion of that point is shm.
[Variations of this kind are said to be sinusoidal because they
are determined by a sine term.]
Snell’s law
At the boundary between any two given materials, the ratio of
the sine of the angle of incidence to the sine of the angle of
refraction is a constant.
71
Item
Definition
Specific heat
capacity c.
The heat required, per kilogram, per degree Celsius or Kelvin,
to raise the temperature of a substance. UNIT: J kg-1 K-1
or J kg-1°C-1
Spring Constant
The spring constant is the force per unit extension.
UNIT: Nm-1.
Strain
Strain is defined as the extension per unit length due to an
applied stress. UNIT: none
Stress
Stress is the force per unit cross-sectional area when equal
opposing forces act on a body.
UNIT: Pa or Nm-2.
Temperature
coefficient of
resistance, .
If the resistance of a conductor at 0°C is R0 and its resistance
at °C is R then  is defined by:
 = (R – R0 ) / R0 . [It is the fractional change in resistance
per degree rise in temperature above 0°C.]
Unit: °C-1
Terminal Velocity
The terminal velocity is the constant, maximum velocity of an
object when the resistive forces on it are equal and opposite to
the accelerating forces (e.g. pull of gravity).
The Law of
Conservation of
Charge.
Electric charge cannot be created or destroyed, (though
positive and negative charges can neutralize each other). In a
purely resistive circuit charge cannot pile up at a point.
The moment (or
torque) of a force.
The turning effect of a force (or moment or torque) about a
point is defined as the force x the perpendicular distance from
the point to the line of action of the force, i.e. moment = F 
d.
UNIT: Nm.
The principle of
moments.
For a system to be in equilibrium,  anticlockwise moments
about a point =  clockwise moments about the same point.
The principle of
superposition.
The principle of superposition states that if two or more waves
occupy the same region then the total displacement at any one
point is the vector sum of their individual displacements at
that point.
The Young Modulus
tensile stress
tensile strain
Unless otherwise indicated this is defined for the Hooke’s
Law region. UNIT: Nm-2
Thermodynamics.
First Law
The heat supplied to a system (e.g. a mass of gas) is equal to
the increase in internal energy plus the work done by the
system. (Q = ∆U + W). [The law is essentially a restatement
of the law of conservation of energy including heat as an
energy form. Any of the terms in the equation can be positive
or negative, e.g. if 100 J of heat is lost from a system
Q =  100 J]
Young Modulus E 
72
Item
Transverse wave
Definition
A transverse wave is one where the particle oscillations are at
90 (right angles) to the direction of travel (or propagation) of
the wave.
73
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Acceleration
Activity
Amplitude
Angular velocity
Area
Avogadro constant
Boltzmann constant
Capacitance
Charge
Charge carrier
density
Current
74
Decay constant
Quantity
Density
Displacement
Distance, length,
height, width
Drift velocity
Electric field
strength
Electric potential
Electromotive force,
EMF
Energy/work done
Extension
Force
Frequency
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
75
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Fringe spacing
Gravitational field
strength
Gravitational
potential
Impedance
Intensity
Internal energy
Internal resistance
Magnetic flux
Magnetic flux
density
Magnetic flux
linkage
76
Mass
Quantity
Molar gas constant
Moment
Momentum
Charge carriers per
cubic metre
Amount of
substance
Number of
molecules
Path difference
Period
Permeability of free
space
Permittivity of free
space
Phase
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
77
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Planck’s constant
Plank constant
Potential difference,
voltage
Power
Pressure
Radius
Reactance
Refractive index
Relative molar mass
Resistance
Resistivity
78
RMS current
Quantity
RMS voltage
Slit width
Specific heat
capacity
Speed
Speed of light
Spring constant
Stefan-Boltzmann
constant
Stiffness
Temperature
Time constant
(capacitance)
Universal constant
of gravitation
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
79
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Velocity
(initial, final)
Volume
Wavelength
Weight
80
Work function
Further Electromagnetism and Alternating Currents
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Self inductance
Reactance
Impedance
Materials
Quantity
Stress
Strain
Extension
Energy density
81
Biological Measurement and Medical Imaging
Quantity
Quantity
symbol
Unit
Unit symbol
Base unit or equivalent
Scalar(s) or
vector(v)
Linear attenuation
coefficient
Acoustic Impedance
82
Absorbed dose
Relationship
Varying
quantities
y 2  kx2  q
x&y
T  2
l
g
T&l
eV  hf  
f&V
E  a  b 2
E&θ
NR 3 M
 2
r4
T
R&T
xy3  kx2  q
x&y
y2
q
 kx3 
x
x
x&y
Plot on xaxis
Plot on yaxis
Gradient
y-intercept
Sketch of graph
83
Relationship
Varying
quantities
f 2  kT
f&T
V
 1
Z 2  R2 
k
l
1
4 c 2 f
2
2
x 2 y  lx  c
x&y
I  knt
y-intercept
Sketch of graph
Z&f
a&g
m
k
Gradient
V&l
a( M  mc )  Mg  k
T  2
Plot on yaxis
T&m
I&n
84

Plot on xaxis
Relationship
q  qo e
t
CR
Varying
quantities
q&t
t
V  Vo e RC
V&t
N  N o e  t
N&t
Plot on xaxis
Plot on yaxis
Gradient
y-intercept
Sketch of graph
85