Course Outline
/HFWXUHV
1. Electrostatics
9
– Stationary charged particles
– Electrostatic forces, fields, potentials
– Analytical methods
640-142 Physics B
2. Circuit Theory
Dr Ann Roberts, PhD
2
– Electrons moving in wires
– Resistors, capacitors, batteries
Dr Robert Scholten, PhD
3. Magnetism
Dr Valerie Gurarie, PhD
11
– Moving charged particles
– Magnetic fields, forces
– Analytical methods
School of Physics
University of Melbourne
http://webraft.its.unimelb.edu.au/640142/pub/
4. Modern Physics
14
© The University of Melbourne 2000
Assessment
Common problems
1. Semester exam
65%
2. Tests
10%
• Vector quantities
• Units
– 30 min short-answer test in week 7 (Sept 4 – 8)
– Exam-style question in week 11 (Oct 16 – 20)
3. Lab work
2
• SI prefixes:
µ = 10-6
n = 10-9
p = 10-12
25%
WARNING! Lecture demos are examinable!
3
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© The University of Melbourne 2000
Resources
Resources
• These lectures, associated notes, old exams, etc:
• The textbook:
Fundamentals of Physics (Extended)
5th Edition, Halliday Resnick & Walker, 1997
http://webraft.its.unimelb.edu.au/640142/pub/
– need Adobe PDF reader
– need activated ITS e-mail account
• Tutorials
• also required for course planning
• Practical laboratory classes
– the web notes alone ARE NOT adequate!
• Your own initiative:
• Lecture times:
A stream (Riv)
9.05 Tues
9.05 Wed
9.05 Fri
4
B stream (Lyle)
11.05 Mon
12.05 Thur
11.05 Fri
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–
–
–
–
C stream(Lyle)
3.15 Mon
3:15 Wed
3:15 Thur
5
Expect 40 hours per week for average mark (“P” grade)
25 points per annum in physics = 25% = 10 hours per week
3 lectures, 3 hours lab, 1 hour tute = 7 hours
3 hours per week, every week (36 per semester) homework!
© The University of Melbourne 2000
6
Some Special Symbols
Introduction
• Industrial Revolution (18th C)
Steam
– Changed nature of work and manufacturing
– Little impact on domestic life
• Non-examinable material
• Electrical Revolution (early 20th C)
Electricity
– Brought benefits to the common person!
– Not clear where this will end yet
!
22
• More conceptually difficult material
• Section reference in text
• First step along the road to a Grand Unified Theory (GUT)
7
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8
© The University of Melbourne 2000
Part 1 - Outline
In the beginning...
Chapter 22 - Electric Charge
• 600 BC – Ancient Greeks discovered lumps of amber,
charged by friction (rubbing) would pick up small
pieces of straw
• Introduction to charge
• Coulomb’s Law
• Greek for amber = “elektron”
• The electric field
• Magnetism discovered about
the same time
• Gauss’s Law
• Electric potential
• Middle-east region called “Magnesia”
• Energy and the electric field
• Applications...
9
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10
© The University of Melbourne 2000
In the beginning...
Now...
• Mid 20th century: Quantum ElectroDynamics (QED)
• 1820 H.C. Oersted: electric current in wire deflects
compass
• Basis of many areas of science, e.g.:
– optics (light = EM wave)
• Late 19th century: Maxwell’s equations combine
electricity and magnetism
– chemistry
– etc.
• 1905 Electricity and Magnetism unified by Einstein
through the theory of special relativity
• Basis of modern technology
– Electric motors to particle accelerators
– This course ends just before 1905!
– Domestic power and communications network
– Global positioning system
– etc. etc. etc.
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© The University of Melbourne 2000
12
The four forces of nature
The four forces of nature
Electric force
Coulomb’s Law 1798
Electromagnetic
force binds atoms
Strong force
binds the nucleus
Electromagnetic
force binds atoms
Gravitational force
Weak force in
radioactive decay
Gravitational force
binds the solar system
Gravitational force
binds the solar system
Newton’s Law
13
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Introductory Electrostatics
22.1
ConcepTest
Three pithballs are suspended from thin threads. Each of
the pithballs is charged by touching it with a previously
charged object (e.g. Perspex rubbed against cat fur, nylon
against silk, glass against polyester, etc.).
• Gravitational “charge” comes in one type
• Electric charge comes in two types
+
It is found that pithballs 1 and 2 repel each other and that
pithballs 2 and 3 repel each other. From this we can
conclude that:
(a) 1 and 3 carry charges of opposite sign
(b) 1 and 3 carry charges of equal sign
(c) all three carry charges of the same sign
(d) one of the objects carries no charge
(e) we need to do more experiments to determine the
sign of the charges
+
Like charges repel
–
–
+
–
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© The University of Melbourne 2000
Unlike charges attract
Pith balls/Electroscope 15
16
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The Naming of Charge
Aside: Introductory atomic physics
• Benjamin Franklin showed
lightning is ordinary electricity
• Negative electrons orbit a
positive nucleus
• Named “positive” and
“negative” charges
• There are the same number of
electrons (-) as protons (+)
• Assumed positive charge was
the one that moved (wrong!!)
• So matter is neutral
–
–
• Can charge matter by adding or
removing electrons
++
++
–
–
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© The University of Melbourne 2000
18
Like charges repel
Introductory electrostatics
• The unit of charge: The Coulomb
+
+
– Charles Coulomb (1736-1806)
+ +
+
• 1 Coulomb = 1 C
• Examples:
+
– Electron charge = –1.6x10–19 C
– Proton charge
= +1.6x10–19 C
– Neutron charge = 0
+
+
+
+
+
+
+
+
+
+
+
Van de Graaf with "hair" 19
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–
Pith balls/Electroscope
20
© The University of Melbourne 2000
Introductory electrostatics
Charge
• The electric force is very strong!
• Usually create charge by scraping electrons from
surfaces
Gravitational attraction negligible
Charge is always conserved
1% charge exchange
+
1% charge exchange leads
to force strong enough to
drag Earth from orbit!
+
+
+
– –
––
Microscopic view of a surface
–
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+
21
3. Cat© The
FurUniversity of Melbourne 2000
Last lecture
22
Hunt for Red October
• Electrostatics: non-moving charge
• Moving objects in dry air become charged
• Charge is:
–
–
–
–
–
positive or negative
like charges repel
opposites attract
unit: Coulomb C
quantised (minimum is e- = -1.6 x 10-19 C)
–
Air flow
–
• Charging by rubbing, e.g. cat fur, helicopter...
–
–
+
+
+
+
+
+
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© The University of Melbourne 2000
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Tragedy of the Hindenburg
Charged Volcanic Ash
• The Hindenburg Zeppelin airship exploded when a
spark from “atmospheric electricity” ignited hydrogen
in the balloon
– 6 May 1937, Lakehurst New Jersey, USA, 36 people killed
+ +
+
++ +
–
+
+
+
+
–
–
–
© The University of Melbourne 2000
25
Conduction of charge
• These “free electrons” can move under the influence
of an electric field ➾ electric current
26
Conduction of charge
+ ++
+
+
+ + +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Uncharged
conductor
Charged
conductor
• There are huge numbers of free electrons available in
an ordinary conductor
– e.g: copper >1022 per cubic cm
• Prevented from leaving surface by electric field of
nuclei
• Other conductors
– Salty water, rarefied gas, flames
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© The University of Melbourne 2000
22.3
• A conductor contains electrons not strongly bound to
any particular nucleus
–
27
Insulators
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Conduction of charge
• Electrons strongly bound to their own nuclei
+ + +
+
+
+ + +
+ + +
• Not free to move
• Glass, chemically pure water, plastics
+
+ +
+ + +
+
+
+ +
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Uncharged
Insulator
Charged
Insulator
• Typically <~ 1 free electron per cubic cm
29
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+
+
+
30
Charging by induction: no touching!
+ ++
+
+
+ + +
+ +
+
+ +
+ +
+
+ +
Coulomb discovers Coulomb’s Law
Uncharged
conductor
Charged
conductor
+
+– – –
–
+
+
+
+
+
–
–
––
+
+
+
– – –
–
–
– ––
Charged
conductor
Charged
conductor
Negatively
charged
conductor
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31
32
© The University of Melbourne 2000
Permittivity of free space
Hydrogen bond in DNA
• The material occupying the space between the
charges influences the strength of the force
• Thymine-Adenine bond via:
O–
• Depends on the permittivity:
N–
H+
H+
N–
N–
• Cytosine-Guanine bond similarly
• Where ε 0 = 8.85 × 10−12 C2 / N m 2 is the permittivity of free
space
• Must replace this with other values if other materials
occupy the space between the charges
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© The University of Melbourne 2000
34
Photocopiers and Laser Printers
Electrostatics in action
(3) Negatively charged toner powder is cascaded over the
surface. It electrostatically adheres to the positively
charged image area making a visible image.
(1) A photoconductive surface is given a positive charge (+).
(4) A piece of plain paper is placed over the surface and
given a positive charge.
(2) The image of a document is exposed on the surface.
This causes the charge to drain away from the surface
in all but the dark areas.
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© The University of Melbourne 2000
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A modern copier
1) document handler
2) photoreceptor belt
3) magnetic rollers apply toner
(5) The negatively charged powder image on the surface
is electrostatically attracted to the positively
charged paper.
4) paper tray
7) output rollers fuse toner
(6) The powder image is fused to the paper by heat.
37
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© The University of Melbourne 2000
How it works
Superposition Principle
See web page for link, or go directly to:
• Big words, simple idea: Add ‘em up!
• Total force from a system of charges is just the sum of the
force from each charge
http://www.physics.udel.edu/wwwusers/watson/scen167/less-copier.html
+
+
+
+
+
+
+
Q
39
© The University of Melbourne 2000
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© The University of Melbourne 2000
Superposition Principle
Vectors
• Total force from a system of charges is just the sum
of the force from each charge
• Each of the force components is a vector
• Vectors must be added vectorially, then final
magnitude calculated
• Example: What is the force on q1?
+
+
Charge = q
+
+
+
y
q3
+
+
ƒ ƒ
2a
x
a
a
–
q2
–
q5
–
q1
a
+
q6
a
–
q4
+
Q
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© The University of Melbourne 2000
42
1996 exam question 1(c)
1(c)
23.1
The Electric Field
sets up
Four equal point charges, +3µC each, are placed
at the four corners of a square that is 40cm on a
side.
Charge
exerts force on
exerts force on
E
Charge
sets up
(i) Using Coulomb’s law and the principle of
superposition, or otherwise, find the force on one
of the charges from the other three
‡6ROXWLRQ
+
‡'UDZGLDJUDP
Direction of E is the
direction a positive
test charge would
move
‡'UDZIRUFHYHFWRUVRQRQHFKDUJHIURPRWKHUWKUHHFKDUJHV
‡5HVROYHIRUFHYHFWRUVLQWRKRUL]RQWDODQGYHUWLFDOFRPSRQHQWV
‡$GGXSFRPSRQHQWV
43
© The University of Melbourne 2000
© The University of Melbourne 2000
44
How big is the electric field?
Electric field for a point charge
•
Inside copper wire of household circuits
•
Charged plastic comb
•
Electron beam in TV; photocopier corona wire
•
Electric breakdown in air
•
Hydrogen atom, at electron orbit radius
•
At uranium nucleus
+
E has magnitude AND direction
at every point in space:
Vector Field
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45
Electric Field from a Dipole
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Why use the concept of a field?
• If we know E at some position, then we know the
force on any arbitrary charge at that position. No
longer need to consider all the other charges that
make the E:
Exercise: Sketch field lines if – replaced by +
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© The University of Melbourne 2000
48
Electric field lines
23.3
Gauss’ Law
• How do we calculate the electric field from a charge
distribution?
• Originate on (+)
charge
• Answer: Use principle of superpostion and integrate!
• Terminate on (–)
charge
+
• But: This to usually too hard!
• Alternative Answer: Use Gauss’ Law
• Lines close
together where E
is strong
+
• Very easy in problems of high symmetry:
–
–
–
–
• Lines far apart
where E is weak
49
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Point charge
Line of charge
Sheet of charge
Often need to find E(r) near these objects!
50
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Gauss’ Law - Introduction
Gauss’ Law - Concept of electric flux
• Field from a point charge:
• Define:
• or
q
Q
Have the area of a
sphere enclosing the
charge!
+
• where Φ is the electric flux
+
E
HOHFWULFILHOG
OLQHV
r
51
© The University of Melbourne 2000
Aside: Special case
(OHFWULFIOX[
LVSURGXFW
RIQRUPDO
DUHDZLWK
HOHFWULFILHOG
© The University of Melbourne 2000
52
Gauss’ Law
• If E and dA are parallel (E normal to surface) then the
flux simplifies:
“The electric flux through a closed surface is equal to
the charge enclosed divided by εo”
• Note that θ = 0 if E and dA are parallel
• So Φ = EA in this case
E
• Useful for finding electric field in problems with high
symmetry
dA
• Rules:
– Decide on direction of E (direction a positive test charge
would move)
– Choose Gaussian surface to make job easiest
– Make sure dA is always either parallel or right angles to E
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© The University of Melbourne 2000
54
Gauss’ Law: point charge
Gauss’ Law: Line of charge
• Use Gauss’ Law to find E at a point distant r from a
point charge q
‡5XOH'UDZE
‡5XOH&KRRVH*DXVVLDQ
VXUIDFHHQFORVLQJFKDUJH
DQGSDVVLQJWKURXJKSRLQW
ZKHUHELVWREHIRXQG
‡$SSO\*DXVV¶/DZ
q
+
© The University of Melbourne 2000
24.3
• Use Gauss’ Law to find E at a point distant r from a
line of charge with λ=q/L Coulombs/metre
E
r
55
24.7
Concept of Electric Flux
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Gauss’ Law
56
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Line of Charge
© The University of Melbourne 2000
58
Concept Test
A cylindrical piece of insulating material is placed in an external electric
field, as shown. The net electric flux passing through the surface
of the cylinder is
1. Positive
2. Negative
3. Zero
Textbook fig. 24.5
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60
24.8
24.8 Gauss’ Law: Sheet of charge
Gauss’ Law: Sheet of charge
Use Gauss’ Law to find E at a point distant r from a sheet of
charge with σ=q/A Coulombs/metre2
Use Gauss’ Law to find E at a point distant r from a sheet of
charge with σ=q/A Coulombs/metre2
Note: E not necessarily
perpendicular for insulator, but
in this case σ is uniform.
WARNING! This is an
insulating sheet of charge
61
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© The University of Melbourne 2000
Internal fields?
Electric Field from a charged conductor
• E field is always
normal to the surface
• E field is always zero
inside
• Why?
+
+
+
+
+
+
––
–
+
++
+
+
+
+
+
63
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External field strength
+
Hollow conductor
+
© The University of Melbourne 2000
(OHFWURPDJQHWLVP
+
+
+
+
+
+
+
+
+
+
+
5HVXOWLVWZLFHDV
VWURQJDVIRUWKHWKLQ
VKHHWEHFDXVHRIWKH
GLVWDQWFKDUJH
64
© The University of Melbourne 2000
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© The University of Melbourne 2000
+
+
Metal ring in petri dish 66
Faraday cage
Faraday cage
• Conductors shield their interior from electric fields
• Conductors shield their interior from electric fields
67
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Radio in shield
© The University of Melbourne 2000
Bare Hands Suit
68
BA009 in Charged Ash Cloud
• Loss of radio signals
+
+
+
+
+
330,000 volt power line
+
+
+
+
Electrically conducting suit: No electric field inside
from Australian Geographic 39: July-Sept 1995 p26
69
© The University of Melbourne 2000
The Electric Dipole
23.9
70
© The University of Melbourne 2000
Polarisation (induced dipoles)
• Since the electric field is so strong, rarely encounter
free charge in nature
• An atom
• More often encounter DIPOLES
H+
Cl–
H+
–
O–
–
H+
+
d
Generic dipole
–
+
–q
+q
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–
71
© The University of Melbourne 2000
72
Polarisation
Lightning
• An atom in an electric field
• A Molecule in a STRONG
electric field
–
–
Need 3 million volts per metre to do this!
Strong Electric
fields break
–
air molecules
–
and causes
sparks!
+
–
–
“SNAP”
+
1H[WWRUTXHRQDGLSROH
73
© The University of Melbourne 2000
Van de Graaf with spark
© The University of Melbourne 2000
74
Lightning
• Just prior to flash, have a line of electrons in a column
between cloud and ground
• λ~ -1 x 10-3 C/m
• Once column bridges gap, e- rapidly
transported:
È current
È e- collisions with air molecules
È ionisation
È further current
• e- + air molecules
È atom excitation
È spontaneous decay
È photons
È flash
75
© The University of Melbourne 2000
Lightning
• λ~ -1 x
10-3
++ + + + ++
–
–
–
–
–
–
–
© The University of Melbourne 2000
76
Lightning
C/m
• Recall for line of charge:
++ + + + ++
–
–
–
–
–
–
–
++ + + + + +
“SNAP”
• Visible luminous part of lightning is typically smaller, ~ 0.5m
– –– – – ––
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© The University of Melbourne 2000
78
Attracting neutral insulators
Attracting neutral insulators
–
–
+
+
+
–
+
–
+
–
79
© The University of Melbourne 2000
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© The University of Melbourne 2000
23.9
Induced Charge
–+
Torque on a dipole
• Dipole in an electric field
+
E
–
Smoke precipitator
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82
© The University of Melbourne 2000
Torque on a dipole
Torque on a dipole
• Dipole in an electric field
• Define the Dipole Moment
d
d/2
Fsinθ
d/2
θ
+
θ
Generic dipole
Fsinθ
E
–
+
–q
+q
p
d
Define p = qd
–
where p is a vector that points from - to +
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© The University of Melbourne 2000
84
Torque on a dipole
Charge and conductors
• Dipole in an electric field
• Take a “pointy” conductor
+
p
Fsinθ
θ
θ
Fsinθ
E
d
–
Conclusion: Dipoles align themselves with E fields
85
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Charge and conductors
+
86
© The University of Melbourne 2000
Charge and conductors
+
+
+
+
+
+
+
+
+
+
+
+
87
© The University of Melbourne 2000
Pointy conductors revisited
+
8. Pointy
object in dish
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88
Sparks and Sharp Points
q1
r1
q2
r2
• Where will the air break-down first?
r1 > r2
All conducting
Connected by conductor so V same
++ + + + ++
Assume separation is large therefore
charge uniformly distributed on each, so:
“SNAP”
–
– –
– –
–
–
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© The University of Melbourne 2000
90
Half Dome - Yosemite National Park
Half Dome - Yosemite National Park
Electric Field
is highest
up here!
++ + + + ++
––
–
– ––
–
© The University of Melbourne 2000
91
© The University of Melbourne 2000
92
93
© The University of Melbourne 2000
94
Half Dome - Yosemite National Park
Electric Field
is highest
up here!
© The University of Melbourne 2000
St Elmo’s Fire
Half Dome - Yosemite National Park
++ + + + ++
Corona discharge
from high fields
at pointy bits
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The Universityin
of Melbourne
2000
9.© Aeroplane
petri-dish
– –
– – –
– –
96
Corona Discharge from BA009
© The University
of Melbourne
2000
Aeroplane
in vacuum
chamber
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