Physics Experiments of the 2nd Semester
Physics teaching organization, NCTU
2010.2
Physics teaching organization, NCTU
Schedule of Physics experiments of the 2nd semester, 2010
Week
Date
Ａ１
Ａ２
Ｂ１
Ｂ２
1
02/21 02/27
Preparation
SA-014
Preparation
Preparation
SA-015
Preparation
2
02/28 03/06 Michelson interferometer
Michelson interferometer
Digital Multimeter Usage
Digital Multimeter Usage
3
03/07 03/13
4
03/14 03/20
5
03/21 03/27
6
03/28 04/03
7
04/04 04/10
8
04/11 04/17
9
04/18 04/24
10
04/25 05/01
Preparation
SA-014
Photoelectric effect
e/m experiment
SA-014
SA-015
Michelson interferometer
Michelson interferometer
Digital Multimeter Usage
Digital Multimeter Usage
Preparation
SA-014
Photoelectric effect
e/m experiment
SA-015
Current Balance
SA-014
Photoelectric effect
e/m experiment
SA-015
Current Balance
SA-015
Current Balance
Preparation
SA-014
Oscilloscope
Preparation
Preparation
SA-015
Hall Effect
RLC Damped Oscillation
12
13
14
15
05/09 05/15
05/23 05/29
SA-014
Oscilloscope
SA-015
Hall Effect
RLC Damped Oscillation
SA-014
Oscilloscope
SA-015
Hall Effect
05/16 05/22
RLC Damped Oscillation
SA-015
SA-014
RLC forced oscillations
Interference and diffraction
Millikan's experiment
SA-015
SA-014
RLC forced oscillations
05/30 06/05
16
SA-015
06/06 06/12 Interference and diffraction
Millikan's experiment
17
06/13 06/19
Interference and diffraction
Millikan's experiment
SA-014
RLC forced oscillations
SA-015
SA-014
RLC forced oscillations
Interference and diffraction
Millikan's experiment
18
06/20 06/26
Final exam
SA-014
Photoelectric effect
e/m experiment
Preparation
SA-015
Hall Effect
SA-014
Oscilloscope
05/02 05/08
Preparation
SA-015
Current Balance
RLC Damped Oscillation
11
Preparation
Final exam
※Each class is named as class A and B and divided in to two group
Final exam
Final exam
Laboratory Regulations
I.
At the laboratory:
1. Before performing the experiment, check and match up the apparatus list and the
apparatus on the table, and please ascertain that nothing is missing. If some apparatus is
missing, please ask your teacher or assistant to help you out.
2. Before manipulating the apparatus, figure out the correct process of operation. If the
apparatus malfunction during the experiment, tell your teacher, assistants or the lab
manager as soon as possible. If the apparatus break down because of the wrong operation,
you have to indemnify the lab for the losses.
3. No chatting, no playing in the lab. Do not treat the experimental apparatus as a plaything.
4. No food, no drinking, except for water.
5. Shut down the cell phone, or set it to quite or vibrate mode.
6. After finishing the experiment, check your result immediately. If the experimental error
is too large, please figure out the reasons and repeat the experiment.
7. Engineering Calculator will help. It is suggested to bring one to class.
8. Never wear slippers or sandals at the lab. It is suggested to wear athletic shoes or leather
shoes.
II. After finishing each experiment:
1. After you finish the experiment, do not clean up the apparatus immediately. After the
assistants or the teacher check you data and sign on your recording book, put the
apparatus in order before you leave the lab. If there is no signature of the assistants or
teacher on your recording book, the effort and score of the experiment won’t be account
this time. If you leave the lab without permission of the assistants or teacher, you will get
the same score with the one absent from the class.
2. After getting the signature of the assistants or teacher, turn off all power, make sure the
apparatus is not lost and works well, and put the apparatus in order. If no apparatus is lost
and works well, sign on the apparatus list and then ask your assistant to sign also. If
taking away any apparatus from the lab, you will be disciplined according to school
discipline.
III. The Remarks of operation of the experimental apparatus :
1. the concept of The use of power:
There are two outlets that divided into voltage 110V outlet and 220V besides
experimental table, please make check how much voltage the instrument needs, then plug
in the plug, to avoid the damage on instruments. Those knobs of the power switch and
degree adjust which are used with instrument in experiment, such as Power Supply. Make
sure everyone bring good habit to longer the endurance of each instrument. For example,
if the experiment requires the power supply 3V, then the correct usage is to switch all
knobs to the minimum, then plug the plug into socket, and turn the switch on, after the
power single lights then adjust the knobs of voltage and current slowly and appropriately
till it displays 3V.If it needs to turn off the power, then go to switch all knobs to
minimum, and then cut off all switch, then unplug the plug. Sometimes precious
instruments need to limit the current of power supply (for example, 0.5A) in order to
avoid that the wire be burned, this time the way of the limitation of current is to make the
power supply circuit shorted out, then adjust the knob of power to 0.5A(since then do not
switch the knob of current), and connect the output to the power resource side on the
equipment that to be used. Then when we keep doing this experiment, no matter how we
adjust the voltage knob, the current of circuit will not surpass 0.5A(current will not be
affected)
2. Attention to the laser safety:
Laser (Laser, called the Light Amplification by Stimulated Emission of Radiation) is an
often applied tool in a laboratory, and it is with a high intensity and the coherent
characteristics. The laser used in this laboratory is the 6328 angstrom wavelength
Helium-Neon laser. Although its power generally does not exceed 5 mW, but because of
its strength is about several hundred times of the sun light, it is still possible to make eyes
injuries, so it should be used carefully. In particular, absolutely it is prohibited to be
used on randomly strafing as a laser gun in the Science fiction movies, and the offenders
will not pass the semester.
3. How should we do if the apparatus do not work?
Based on past experience, there were more than half of the cases equipments would not
work because the power has not been turned on (forgot to open?),or forgot to plug the
plug of instrument into socket, then the second comes to the equipment assemble, or
connecting problems exist. So next time you find that equipments do not work, please do
not look for assistant very soon, try to develop the ability of discovering the reason which
makes instruments does not work (the debug ability will be helpful to their own future
development) by the fore said two points , after you make sure it is not caused by the
above reasons by check again, then consider it is the equipment's fault.
IV. The Remarks of the absent caused of personal reason:
1. In order to implement the teaching philosophy that each and every course students must
do the experiment, students must have completed arrangement for each experiment
personally.
2. If you have personal reason to not attend the certain class, you need to be in advance to
tell assistants in face or telephone contact to do a formal absence before class (it is
invalid if it is informed by the other classmates), besides obtain the permission of
assistant and the consent, and arrange another time for experiments in the same time.
3. If you failed to do a advance before leaving, you must give the guide teacher or assistant
the reasonable proof otherwise you shall not make up for the experiment ,if the reason
can be accepted ,students may be granted up assistant for the experiment, but student
must complete it within the allowed time.
4. The one who missed the experiment, the quiz of the result report of experiment are zero,
with second miss of the experiment classes, all total score of experiment are failed.
V. Final semester class grades
1. Preview report
20%
2. Recording book
45%
3. Final exam
25%
4. In-class
10%
z You have to hand in the preview report at the beginning of the class. If not, you can’t
initiate the experiment.
z If you copy the data and reports from others or cheat in an exam, the report or exam won’t
be scored. If the situation is serious, you will fail in the class.
z If you don’t hand in the recording book before the deadline, you will get zero point. If the
recording book was not hand in on time and accumulating up to two times, you will fail in
the class.
Contents and Forms of Report and Recording book
I.
Preview report:
Read the manual and write a preview report. Some video may be helpful for you, and
you can download them on homepage of NCTU’s general physics education.
(http://140.113.28.5)
1. Contents of preview report：
(1) Remarks (attention items)
(2) What is the purpose for every subsection of the experiment?
(3) What are you supposed to measure in the experiment?
(4) What physical parameters do you have to verify finally? Explain how to calculate
these physical parameters.
(5) What are the theoretical values (calculating values) of those physical parameters
that you have to calculate in the above question?
(6) Answer some questions in the manual.
(7) Reference (Optionally)
2. You may use single or double print, please do not use red print. Only handwriting is
acceptable.
3. Paper size：A4
4. Please write down your class, team number, student ID, and name on the right-top
corner of the first page. And write down who your partner is.
Ex：
EE1Ａ
13th team
9411054
Ding, Xiao-yu
5. The way to note your reference：
D .Halliday & R .Resnick：Fundamentals of Physics, 2nd ed. （John Wiley & Sons, Inc.,
New York, 1981）, chap.5, p.57.
S. C. Wu and C. A. Barnes, Nuclear Physics, A422, 373（1984）
II.
Recording book:
1. Contents of recording book:
(1) Data
(2) Answering the questions in this book
(3) Discussion the result (Optionally)
(4) Conclusion
2. For students who draw the diagram in hand-written form, please use section paper.
3. Please do the curve fitting for your data, calculate the expecting quantity, and calculate
the inaccuracy.
4. The result of the data should be in the form of X ± σ X with units.
5. We suggest you to use computer (Ex: MS-Excel, SigmaPlot, xmgr, origin …) to do the
statistics analysis, curve fitting, calculate the standard deviation, and draw the diagram.
Table of Contents
Unit
Topic
Unit 1
Michelson Interferometer
1-1
Unit 2
Digital Multimeter Usage
2-1
Unit 3
Photoelectric Effect
3-1
Unit 4
Charge to Mass Ratio of An Electron
4-1
Unit 5
Current Balance
5-1
Unit 6
Oscilloscope
6-1
Unit 7
RLC Series Circuit
7-1
I.
7-1
Damped Oscillations
Page
II. Forced Oscillations
7-7
Unit 8
Hall Effect
8-1
Unit 9
Interference and Diffraction
9-1
Unit 10
Millikan's Oil Droplet Experiment
10-1
Unit 1 Michelson Interferometer
Remarks:
1.
2.
3.
4.
5.
6.
Please note that laser radiation is harmful. Do not stare into beam.
Do not bend over the table during the experiment. Since your eyes may exposed
around laser beam.
Make sure your laser beam won’t hurt anyone else. When you are moving a laser,
please block the beam or turn it off first.
During observation, do not moving around in order to prevent any vibration. It may
influence your observation.
Do not touch the surfaces of any optical instruments (beam-splitter and mirrors).
If the fringes are not perfectly circular, it would not influence the measurement of
number n.
Keywords
Michelson, Wave Optics, Interference, Coherence, Temporal Coherence, Beam-splitter,
He-Ne Laser
Objectives
Study the theory and the design of Michelson Interferometer. And use it to measure the
wavelength of a light source.
Apparatus
Michelson interferometer, He-Ne Laser (λ= 6328 Å), Beam-splitter, Screen
Principles British scientist Thomas Young did the experiment about interference in 1800. It was the
first investigations about light interference. He let the light pass through two closely spaced
narrow slits. The light would split into two parts, which is so called division of wave front. He
saw the fringes on the screen at some distance behind. In order to explain this result, Thomas
Young established the theory of wave optics.
Besides, using beam-splitter is another way to split the amplitude into two parts. This is
so called division of amplitude which is the idea used to design the Michelson Interferometer.
1-1
Screen
S
Adjustabble mirror
L2
45∘
2
45∘
Light source
B' A
P
Beam-splittter
Leens
1
L1
B
F
Fixed
mirror
Fig.1 Mich
helson Interferometerr
Ass shown in figure
f
1, a divergence
d
s
spherical
waave is formeed by usingg a convex lens. The
light inccident on thhe beam-spllitter P is diivided into two
t
beams. One beam, labeled as Beam1,
is refleccted to fixeed mirror B which refflects the beeam back again
a
and thhen passes through
beam-spplitter P, finnally, arrivess at the screeen S. The other
o
beam, labeled as Beam2, wo
ould pass
throughh the beam--splitter P first and thhen reflecteed back byy adjustablee mirror A. Again,
beam-spplitter P willl reflect this beam to thhe screen S..
Whhen Beam1 and Beam
m2 overlap on
o the screeen S, if the optical patths of two beams
b
is
differennt (i.e.
), it wouuld cause innterference fringes. If
, tthe virtual image
i
B'
formed by beam-ssplitter P would lies inn front of A.
A The pathh differencee B'A is thee reason
causes interferencee. If B' andd A is perffectly paralllel, the frinnges wouldd become perfectly
p
concenttric circles, as shown in
i figure 2.. As A approaches B',, the numbeer of fringees would
decreasee. If B' oveerlaps A, frringes woulld disappeaar and replaaced by a bbright region
n on the
screen. If B' and A are not perffectly paralllel, the fring
ges would be
b oval-shapped.
Fig.2 conceentric circu
ular fringess
1-2
Screen
Beam-splitter
A
P
Adjustable
mirror
Fixed
mirror
He-Ne laser
Lens
Screws
Screw micrometer
Fig.3 Experiment set-up
Instructions 1.
2.
3.
4.
5.
6.
7.
8.
Place the He-Ne laser in front of the lens part of the interferometer as shown in figure 3.
Turn on the laser. Adjust the holder of laser or you can also adjust the horizontal level of
interferometer to let the laser beam goes through the beam-splitter and then arrive the
center of adjustable mirror. (Do not let the reflection of lens directly incident back into
aperture.)
Adjust the beam-splitter to let the reflection meet the center of fixed mirror.
Now you would see two spots on the screen. One comes from the adjustable mirror; the
other comes from the fixed mirror. If not, adjust the screws on the fixed mirror to let the
reflection goes back through the beam-splitter and then arrive the screen.
Keep adjust the screws to let the spot, which comes from the fixed mirror, overlaps the
other one.
Now you may see some fringes. Keep adjust the screws carefully to let the center of
fringes can be seen clearly on the screen. (Even more, a perfect circular fringes.)
Move the adjustable mirror back and forth by adjusting the screw micrometer. You may
see the movements of the fringes.
The displacement of the adjustable mirror is one twenty-fifth of the displacement of the
screw micrometer. If you turn the screw micrometer in 5 ticks, for example, the
displacement of adjustable mirror is:
5 ticks
9.
0.01
0.002
Note that the optical path difference is twice of the displacement of mirror. (i.e.2 )
Record the change number of the fringes n, and also the displacement of adjustable
mirror d. Determine the wavelength of the laser by using the equation 2
10. Repeat step 9 for at least 4 times. (i.e. at least five data)
1-3
.
Questions Q1: What is the full name of LASER?
Q2: What is the difference in theory about light splitting between Young's and
Michelson interference?
Q3: What are the applications of Michelson Interferometer?
Q4: In some light spectrum experiments we use some kind of tool to split light. Can you
tell difference between that and the beam-splitter which is used in this experiment?
Q5: Please refer to the general physics textbook. Please describe what Coherence is?
What's the difference between Spatial Coherence and Temporal Coherence?
Q6: What is the advantage of using Laser? (In other words, why do we choose He-Ne
Laser as light source?)
1-4
Unit 2 Digital Multimeter Usage
Remark:
1.
2.
3.
The rotary switch should be placed in the right position and no any changeover off of
range shall be made during measurement is conducted to prevent damage of the
Meter.
Turn the Meter off when it is not in use.
Disconnect circuit power and discharge all high-voltage capacitors before testing
resistance, continuity, diodes and current.
Key words
Ohm’s law, Digital multimeter, Ammeter, Voltmeter, D'arsonval galvanopmeter
Objective
In physic experiments, we usually use some basic instruments to measure the physics
quantities. Measurement of current and voltage are the most common methods. Therefore, in
this experiment, we would like to introduce modern digital multimeter which can measure
current and voltage. And let you learn the basic concept of measurement, alternating current,
and direct current so you can have solid background to do the rest experiments in this
semester.
Apparatus
Digital multimeter, Resistance, Direct current power, Alternating current power
Principle
The function of a multimeter is to measure the current, voltage, and resistance. It's a
combination of an ammeter and a voltmeter. With Ohm’s law, we can know the resistance of a
resistor by measuring the current under specific voltage.
The design is based on D'arsonval galvanopmeter. The followings are principles of kinds
of measurements.
Permanent magnet
久磁鐵
Upper spring
Indicator
Flexible cooil
iron
N
S
S
N
iron
Lower spring
(a) End view (b) 3D picture
pivot
Fig.1 D'arsonval galvanopmeter
2‐1 Magnet with plot of magnetic line
N
S
(a) iron
Torque L1
Magnet with plot of
magnetic line
Current flow outward
N
(b) S
Current flow
inward
iron
Fig. 2 Principle of D'arsonval galvanopmeter
（I）Principle of D'arsonval galvanopmeter
The structure of D'arsonval galvanopmeter is shown in Fig.1. As shown in Fig.2 in a top
view, when current I pass through flexible coil, it generates magnetic field. This generated
magnetic field in the permanent magnet would cause a clockwise torque L1 . The torque would be
in proportion to the current I, i.e.
L1 = K1 I
where K1 is the proportion constant.
This torque would cause the rotation of the coil. Upper and lower springs causes the
anticlockwise torque L2 , i.e.
L2 = K 2θ
When two torques L1 , L2 meet a balance, the coil would stay at a specific angle θ, i.e.
L1 = L2
or K1 I = K 2θ
2‐2 Assume K =
K2
, we can get I = K θ . Therefore, the amount of current can be read by
K1
measuring the angle of the indicator.
Generally, power supply can be divided into two kinds: direct current and alternating
current. The current and voltage of direct current always stay constant. They would not vary
with time. The current and voltage of alternating current would vary cyclically with time.
Thus, the circuit would act differently when you supply these two kinds of power source. To
explicate the differences, take electric power as an example:
(1) If a resistor is supplied by direct current, the average power P would be:
P = I 2R
(2) If a resistor is supplied by alternating current I=ImSin (2πt/T)
current and T is the period), the average power P would be:
P=
RI
1
t
RI m 2 sin 2 (2π )dt = m
∫
0
T
T
T
T
2
=
RI m t
( −
T 2
2
∫
T
0
1 − cos
2
(Im is the maximum
4πt
T dt
4πt
2
2
T ) |T = RI m ⋅ T = RI m = R( I ) 2
rms
0
8π
T
2
2
T sin
You can see that the average power of alternating current has an additional factor 1/2. In
order to unify the formula of alternating current and direct current, we define an effective
current (root mean square of current) to describe the total effect of alternating current:
I
I rms = m = 0.707 I m . Similarly, we can define an effective voltage (root mean square of
2
voltage). When measuring the alternating current, the amounts shown on multimeter are I rms
and Vrms .
（II）Ammeter – current measurement
As shown in Fig. 3, when a galvanometer is used as an ammeter, a shunt resistor R is
connected in parallel with the galvanometer.. Assume the internal resistance of galvanometer
is Rg , the maximum direct current which passes through the ammeter is I, and the maximum
direct current which passes through the galvanometer is I f . The amount of the shunt
resistance S can be determined by:
2‐3 Rg I f = (I − I f )S
∴S =
If
I − If
×R g
DC Ammeter
Galvanometer
G
If
a
S
b
I
Fig. 3 DC ammeter
AC ammeter
Rectifier
Galvanometer
G
If
a
S
b
I
Fig. 4 AC ammeter
Thus, the measuring range of the DC ammeter can be various with different shunt
resistance S.
For AC ammeter, it is formed with a galvanometer, a small resistor, and a rectifier. (A
diode has the characteristic of low resistance under forward bias and high resistance under
reverse bias.) Since D'arsonval galvanopmeter can only work with direct current, a rectifier is
required to transform alternative current into direct current. Insert a rectifier into the left side
of node a in Fig. 3 and it can be an AC Ammeter. But please remember that the dial scale of
1
an AC ammeter is the peak current time 0.707（ =
）.
2
2‐4 （III）Voltmeter – AC and DC voltage measurement
DC voltmeter
G R
Rg
I
V
Fig. 5 DC voltmeter
As shown in Fig. 5, when a galvanometer is used as a voltmeter, a resistor R is connected
in series with the galvanometer. Assume the highest voltage measured by galvanometer is Vm ,
the current at this time is I m , the internal resistance of the galvanometer is Rg and the highest
voltage to measure is V (= Vm N ) , the resistor we need to connect in series, R, can be
determined by:
Vm = Rg I m
V = NVm = ( R + Rg ) I m
NRg I m = ( R + Rg ) I m
R = ( N − 1) Rg
For AC voltmeter, it would be the same as DC voltmeter except it requires one more
rectifier and the dial scale is defined by multiplying 0.707.
(IV) Resistance measurement
With Ohm’s law, we can know the resistance by measuring the current under specific
voltage. The amount of resistance can be determined as the following:
R=
V
I
2‐5 Instructions Preparation: Panel descriptions of the digital multimeter are showed below.
Fig.7 Digital Multimeter
(I) Rules for safe operation:
1.
2.
The rotary switch should be placed in the right position and no any changeover off
of range shall be made during measurement is conducted to prevent damage of the
Meter. Use the proper terminals, function, and range for your measurements.
Insert the red test lead into the VΩmA terminal and the black test leas into the
3.
COM terminal.
Turn the Meter off when it is not in use.
(II) DC current measurement
1.
2.
Connect the resistor to the power supply.
To measure current, do the following:
a. Set the rotary switch to an appropriate measurement position in A L range.
b. Break the current path to be tested. Connect the red test lead to the more positive
side of the break and the black test lead to the more negative side of the break.
2‐6 c. Turn on power to the circuit.
d. Read the measured value shows on the display.
3.
Use Meter to measure the resistance and the voltage across the resistor. Calculate
the current. (Remember to turn the power supply off when you measure the
resistance with multimeter.)
Q1：Are the currents read in step 2-d and calculated in step 3 the same? If not, why?
(III) AC Voltage Measurement:
1.
Set the rotary switch to an appropriate measurement position in V～ range
2.
Insert the red test lead into the VΩmA terminal and the black test leas into the
3.
COM terminal.
Connect the red test lead to the positive and the black test lead to ground terminal of
the main output of the function generator. First, set the frequency at 60Hz to
simulate ordinary AC power. Adjust amplitude control of the function generator,
measure AC voltage.
Q2：In step 3, what is the maximum voltage you measured?
4.
Set the output amplitude control to center, measure AC voltage with various
frequency. (60Hz、120Hz、1kHz、10kHz、100kHz、1MHz)
Q3：In step 4, are the AC voltages you measured in different frequencies the same?
2‐7 Unit 3 Photoelectric Effect
Remarks:
1.
2.
3.
The light spectrum of the mercury vapor light source contains ultraviolet spectrum. Do
not stare into the light source directly.
Turn off the mercury vapor light source after you finish the experiment.
For apparatus maintenance, please close the mask of the photodiode after measuring.
Keywords
Photoelectric Effect, Work Function
Objectives The issue of black body radiation is where the revolutionary quantum mechanics begins.
Then the foundation of quantum mechanics consolidates by several famous experiments. One
of the famous experiments, also is the start of the understanding to the whole story, is
photoelectric effect. In this experiment we observe the phenomenon of the electron emitted
when light with different energy strikes the Cs3Sb metal slab. By understand the principle of
photoelectric effect we can also derive the Plank’s constant h.
Apparatus
Photoelectric effect experiment instrument, Mercury vapor light source, Yellow light
filter, Green light filter, Digital voltmeter, Variable transmission filter
Photoelectric
effect experiment
instrument
Digital
voltmeter
Light
splitter
Mercury vapor
light source
Filter
Fig.1 Experiment set-up
3-1
Principles
When we shine the light, the wavelength of which is longer than a specified amount, on
the surface of the metal, there would be no electron emitted to induce the photo current even
we increase the intensity. This is the phenomenon that the classical wave model can't explain.
Einstein applied the idea of light quanta to explain the photoelectric effect in 19th century.
Einstein pictured a wavefront of light as consisting of billions of photons. He assumed that the
energy of a single photon is
, where
is the frequency of the light. The total energy
is
n , where n is the number of photons. When n is large means the intensity of the
light is high.
The electrons would be emitted only when a single photon of the light has energy high
enough. In the process of photoemission, when the light shines the surface of the metal, a
photon gives up all its energy to a single electron. As a result, the electron is ejected
instantaneously. The maximum possible kinetic energy of the photoelectrons is determined by
the energy of each photon minus the work function , which is the minimum energy needed
to extract an electron from the surface of the metal.
Suppose light strikes a metal plate (emitter) in the photoelectric tube shown in figure 2.
The emitted photoelectrons, which have kinetic energy, moving to the collector constitute a
current in the circuit; that is so called the photo-current. If we applied a potential difference
between the emitter and the collector, it would repel some of the photoelectrons from
reaching the collector and decrease the photo-current. Once the potential difference just repels
the photoelectrons which have the maximum kinetic energy, at this very moment the
photo-current become zero. This potential difference
related to the incident light through the relationship:
eV0 = hν − φ
is called the stopping potential and
In this experiment, we can derive the work function of the metal plate and explain the
photoelectric effect by measure and record the relationship between the stopping potential and
the frequency of incident light.
Photons
_
+
emitter
collector
V
Fig.2 Photoelectric tube
3-2
i
G
Q1: Explain the wave theory, the particle theory and wave-particle dualism of light.
What experiments supports those theories?
Instructions 1.
2.
Experiment set-up as shown in Figure 1.
Check the batteries: Connect the OUTPUT ground terminal and each BATTERY TEST
terminal (-6V MIN and +6V MIN) by digital voltmeter. If either battery tests below its
minimum rating means you should have new battery changes before starting the
experiment.
Light Shield
Battery Test
Reset
Window
Ground
Power Switch
Mask
Fig.3 Photoelectric effect instrument
Note: Keep in darkness in order to avoid the influence from other light sources.
A.
Change lights with different frequency, and measure the stopping potentials.
1. Turn on the mercury vapor light source and wait for several minutes until you can
see several orders of diffractions which consist of five different spectral colors.
(The wavelength of each spectrum is shown in Table 1.) Choose the first order of
diffraction as the light sources.
2. Open the light shield of the apparatus. Make sure that only the yellow band enters
the window and shines on the photodiode.
3. Place the yellow colored filter over the mask. Before you close the light shield to
prevent influence, make sure that the incident light shines on the photodiode.
4. Press the reset button, the stopping potential will be generated by the internal circuit
of the instrument and shown on the digital voltmeter. Wait until the reading do not
change (about 1~2 minutes), record the stopping potential.
5. Repeat step 2~4 to measure the stopping potential of every different color lights.
Note that it is necessary to place green colored filter when measuring green light,
neither to other bands.
3-3
Q2: What do we use to split the light? Is there any other way to do this?
Q3: Why do we place the filter only when measuring yellow and green bands?
6.
Plot the stopping potential V0 versus the frequency of incident light v. Extend the
line to make the line intersects with the v axis. (Fig 4.)
ν0
Fig.4 Stopping potential versus frequency
Q4: How to get the Plank’s constant h from the figure of stopping potential V0 versus
the frequency v? Is your result agreed with that of the text book?
Q5: How to get the work function from the intercepts of x and y axes in figure 4? Is the
work function you derive the same as the work function of Cs3Sb metal plate (1.36±
0.08 eV)? If not, try to find any explanation.
B.
Change the intensity of the light source
Observe the relationship between the stopping potential and the intensity of the light
source.
1. Place the variable transmission filter, as shown in figure 5, in front of the mask.
First let the incident light passes through the section which is marked 100%. Record
the stopping potential. (Also, wait about 1~2 minutes for stable readings.)
2. Adjust the variable transmission filter and record the stopping potential for 80%, 60%,
40% and 20%.
3. Choose three different light bands, repeat step 1~2.
Q6: What is the conclusion from comparing the stopping potential under different
intensities of the light? Does it agree with the theory? Why?
Q7: What achievements did Einstein made and awarded the Nobel Prize?
3-4
20
40
60
80
100
Relative Transmission (%)
Fig.5 Variable transmission filter
Appendix Color
Frequency (1014Hz)
Wavelength (nm)
Yellow
Green
Blue
Violet
Ultraviolet
5.18672
5.48996
6.87858
7.40858
8.20264
578
546.074
435.835
404.656
365.483
Table 1. Wavelength of different light sources
material Work Function (eV) material Work Function (eV) material Work Function (eV)
Ag
4.26
Al
4.28
As
4.79
Au
5.1
Ba
2.52
Bi
4.34
Ca
2.87
Co
4.97
Cr
4.44
Cs
1.95
Cu
4.65
Fe
4.6
Ga
4.35
Ge
5.15
In
4.08
K
2.3
Mn
4.08
Mo
4.49
Na
2.36
Ni
5.15
Pb
4.25
Pd
5.4
Pt
5.63
Rb
2.05
Ru
4.71
Sb
4.56
Si
4.95
Sn
4.28
Ta
4.3
Ti
4.33
U
4.33
W
4.55
Zn
3.63
Table 2. Work function of different materials
3-5
Unit 4 Charge to Mass Ratio of An Electron
Remark:
1.
2.
3.
4.
Before turning on the power, make sure that the voltage and current controls are both
turned down to zero. Set the voltage and the current after pre-warming for 5 minutes.
When finishing the experiment, turn the plant voltage and the current to zero, then turn
the power switch to "OFF".
If the operation lasts over one hour, take a rest for a while.
Slowly vary the plate voltage to prevent damage to the apparatus.
Keywords
J. J. Thomson, Lorentz Force, Magnetic Fields
Objective
To determine the charge to mass ratio of an electron.
Apparatus
e
apparatus.
m
Principle
In 1897, J.J. Thompson set out to prove that the cathode produced a stream of
negatively charged particles called electrons. The beam of electrons in the tube is produced by
an electron gun composed of a heated filament. Moving charged particles could be deflected
e
in a magnetic field. It provide a method of measuring
, charge to mass ratio of an electron.
m
In 1909, Robert Millikan determined the elementary charge e. Then using Thompson's value
e
of
.
, he calculated the value of
m
r
The magnetic force acting on a charged particle of charge q moving with velocity ν in
r
a magnetic field B is given by
v
v v
F = qv × B
(1)
4-1
Fig. 1
As shown in figure 1, the magnetic field vector is perpendicular to the paper surface, directed
r
out of the paper; and the charged particle velocity is perpendicular to B . Eq. 1 can be written
v
in scalar form as F = qvB. According to the "right-hand rule", the force F is perpendicular
r
to ν . It implies that the particle trajectory is circular, and the particle must be experiencing a
centripetal force of magnitude
F =m
v2
r
(2)
Where m is the particle mass and r is the radius of the circular motion. Assume that the
moving particle is an electron with the charge e. Combine Eq. 1 with Eq. 2, we can get the
equation
v2
m
= Bev
r
(3)
Assume that the electron is initially at rest and is accelerated through an electric potential
difference V. The electron has a kinetic energy
eV =
1 2
mv
2
(4)
Substitute Eq. 4 into Eq. 3, we can get the charge to mass ratio of the electron
2V
e
= 2 2
m B r
(5)
In this experiment, the uniform magnetic field is generated by Helmholtz Coils. As
shown in Fig. 2, Helmholtz Coils are a pair of flat circular coils, with equal numbers of turns
4-2
and equal diameters, arranged with a common axis and connected in series. They generate a
nearly uniform magnetic field, parallel to the center line of two coils. The magnetic field is
given by
B=
8μ 0 Ni
(6)
125R
N = 145
R = 14 cm
μ 0 = 4π × 10 −7 Weber/amp.m
Where N is the number of turns of one coil, R is the mean radius of the coil, i is the current
through the coils and μ 0 is the permeability of free space. Combining Eq. 5 with Eq. 6 yields
e
125R 2V
=
m 32 μ 0 2 N 2 i 2 r 2
(7)
e
apparatus
m
The lamp power switch used to heat the filament
The plate voltage power switch used to accelerate the electrons
The magnetic field power switch
Fig. 2 The connection of
S1：5 V
S2：0~300 V
S3：0~20 V
4-3
Fig. 3
e
apparatus
m
Instructions
I.
The incident electron beam is perpendicular to the magnetic field.
1. The apparatus is shown in Fig. 3. After making sure that the voltage and current
controls are both turned down to zero, turn on the power. Set the deflector voltage
to OFF. Set the current direction in the magnetizing coil to CLOCKWISE. Slowly
turn the plate voltage control clockwise to increase the voltage until an electron beam
appears.
2. Set the plate voltage to 150V. Find the radius of the electron beam with the current in
the range of 0.9A ~ 1.4A. Repeat 10 times with different currents. Plot the graph of
e
1
versus current. Find the slope of the curve to determine
.
m
r
Q1: How do you measure the radius of the electron beam? What are the merits and
demerits of your method? Suggest at least two reasons causing the error in the
measurement.
4-4
3. Set the magnetizing current between 1.0 and 1.2A. Keep the magnetizing current
constant. Find the radius of the electron beam with the plate voltage in the range of .
(The voltage range from 150V to 300V) Plot the graph of r 2 versus voltage. Find the
e
slope of the curve to determine
.
m
e
of each measurement in Step 2 and Step 3. Calculate the average and
4. Calculate
m
the standard deviation of mean.
II. The incident electron beam is not perpendicular to the magnetic field.
1. Set the voltage between 150V and 300V and the current between 1.0~1.2A. Keep the
voltage and current constant.
2. Find the radius of the electron beam with the incident angle θ of the electron beam.
Repeat 10 times with different incident angles.
e
1
3. Plot the graph of versus sinθ. Find the slope of the curve to determine
.
m
r
Questions
Q2: What is the theoretical value of
e
?
m
Q3: How will the electron beam be when you vary the plate voltage?
Q4: How will the electron beam be when you vary the magnitude and the direction of
the magnetizing current?
Q5: Why can you see the electron beam? Does the glass tube enclose a vacuous?
Q6: Why is the electron beam green? Is it possible to make a change to the color of the
electron beam?
Q7: Is the trajectory of the electron beam influenced by terrestrial magnetism or
gravitation?
4-5
Unit 5 Current Balance
Remarks:
1.
2.
3.
4.
5.
6.
Be careful. The probe of the Tesla Meter is Fragile and very expensive.
Before turning on power switch, insert the sensor probe first. Check the installation
direction for the probe before inserting it.
Before using Tesla Meter, check the instruction manual to learn how to reset it to zero.
Before using the electronic scale, make sure that the scale is in a horizontal position.
Never weigh any object which will exceed the capacity of the electronic scale, which
is about 600 grams. Do not put the object on the scale for a long time.
The maximum load of the Current Loop PC Board is 2A, the maximum load of the
Current Balance Accessory Unit is 5A, and the maximum load of the power supply is
3A. Please avoid overloading the current, so that the instrument won’t be damaged.
Keywords
Lorentz force, Ampers’ right hand rule
Objective
Denmark scientist Hans Christian Oersted accidentally found that the current-carrying
wire would affect the pointing direction of the compass. Furthermore, due to the effort of
Jean-Baptiste Biot, Felix Savart, Andre-Marie Ampereand, Michael Faraday, the secret
relationship between the electricity and magnetism was revealed, which established the
foundation of the current electrical engineering. By analyzing the relationship between the
force on the current-carrying wire in the magnetic field and four variables - wire length,
strength of the magnetic field, magnitude of current and the angle between the wire and the
magnetic field, this experiment tries to make you experience what their experienced and then
realize the wonders of the electricity and magnetism.
Apparatus
One Main Unit, six Current Loop PC Boards, two sets of magnet assemblies (one with
six U magnets, one with five square magnets) (Fig. 1), one Current Balance Accessory Unit
(Fig. 2), one electronic scale, one power supply, one multimeter, wires, one base and support
rod, one Tesla Meter, 12 tack-shaped magnets (optional) and one compass.
5-1
Power Supply
Main Unit
Electronic Scale
Current Balance
Accessory Unit
Magnet Assembly
Current Loop PC Board
Figure 1. Apparatus
Probe
Tesla Meter
Zero Flux Chamber
Figure 2. Tesla Meter
5-2
Magnet
Assembly
Figure 3
Tesla Meter
Instruction Manual of the Tesla Meter：
I.
II.
III.
Power: You should insert the probe, before you press the POWER switch (1).
Selection of measurement units: Rotate the function selector (4) to UNITS, press
SELECT (2) and select the unit you need. The unit needed in this experiment is “T”.
Range selection：Rotate the function selector (4) to RANGE, press SELECT (2) and
select “AUTO RANGE”.
Zeroing: Rotate the function selector (4) to ZERO, insert the probe into the ZERO
IV.
FLUX CHAMBER, and press RESET (3) to zero it.
Measurement of the magnetic field: After zeroing process, rotate the function selector
(4) to MEASURE and put the probe into the magnetic field which we want to
measure. The Tesla Meter can only measure the magnetic field which is perpendicular
V.
to the surface of the probe, and the sensor is placed in the peak of the probe.
Therefore, you should pay attention to the position of the probe. The principle is in
Unit Eight “Hall Effect”.
(Notice: The probe is fragile. Be careful to use it.)
5-3
Principle
Based on the investigation of Lorentz, the force on the current-carrying wire in the
magnetic field is
F = iL×B or
F = iLB sinθ
Thus, based on the preceding equation, the magnitude and the direction of the force depends
on four variables：
(1) the magnitude of the current I
(2) the length of the wire L
(3) the strength of the magnetic field B
(4) the angle θ between the wire and the magnetic field
You can vary the variables in the equation and measure the resulting magnetic force to
verify Lorentz’s force equation.
Instructions
(1) The relationship between the force on the wire and the magnitude of the current i
1. Set up the apparatus as shown in Figure 4. Plug the sixth Current Loop PC Board
into the ends of the arms of the Main Unit, with the foil extending down. Let the
horizontal portion of the conductive foil on the current Loop pass through the pole
region of the magnets. Notice: The Current Loop shouldn’t touch the magnets. Zero
the indicator of the power supply first. (Make sure the direction of North and South
poles of the little magnets are the same when putting them on the magnet
assembly.)
2. Measure the strength of the magnetic field B in the indentation of the magnet
assembly with the Tesla Meter.
3. Determine the weight of the magnets while no current flowing. Mark this value as
W1.
4. Set the current to 0.3A and Determine the new “weight“ of the magnet assembly.
Mark this value as W2.
5.
6.
The difference of W1 and W2 is force.
Increase 0.2A each time (the maximum of current is 2.0A) and repeat steps 2-4
eight times (i.e. 9 times in all) Plot a graph of force F versus current i.
Q1: As the apparatus (Fig. 4) is power-on, would you be in danger of an electric shock if
touching the ends of the arms of the Main Unit?
5-4
Main Unit
Current Loop PC Board
Magnet Assembly
Power Supply
Electronic Scale
Figure 4
(2) The relationship between the force F on the current-carrying wire and wire
length L.
1. Set up the apparatus as shown in Figure 4. Measure the strength of the magnetic
field B in the indentation of the magnet assembly with the Tesla Meter.
2. Determine the weight of the magnets while no current flowing. Mark this value as
W1. Fix the current and determine the new “weight“ of the magnet assembly. Mark
this value as W2. The difference of W1 and W2 is force.
3. Vary the wire length by using one of the six different Current Loops. Determine the
new “weight” of the Magnet Assembly.
4. Plot the graph of force F versus the length of the wire L.
(The wire length is at the appendix.)
(3)The relationship between the force F versus the strength of the magnetic field B.
1. Use the Tesla Meter to measure the strength of the magnetic field B.
Q2: How to determine the North and South poles of the magnet with Tesla Meter?
Q3: Is the magnetic field in the Magnet Assembly well-distributed?
2.
Set up the apparatus as in Figure 4. Select the fourth current loop PC board and plug
it into the ends of the arms of the Main Unit.
Q4：Compare with other current loop PC boards, what’s the advantage to use the 4th one
here?
5-5
3.
Mount the single magnet in the Magnet Assembly.
4.
Determine the weight of the magnets while no current flowing. Mark this value as
W1.
Set the current to 1.5A. and Determine the new “weight“ of the magnet assembly.
Mark this value as W2.
The difference of W1 and W2 is force.
Add one more magnet at one time. Repeat step 1-6. Plot the graph of force F versus
the strength of the magnetic field B. (Use tack-shaped magnets to increase the
magnitude. Make sure the direction of North and South poles of the little magnets
are the same when putting them on the magnet assembly.)
5.
6.
7.
Q5: Is the magnitude of the magnetic proportional to the number of the magnets?
Q6: In (3), if only 2 magnets are placed on the Magnet Assembly, does the position of the
magnets affect the result?
(4) The relationship between the force F versus the angle θ.
1.
Set up the apparatus as shown in Figure 5. Measure the strength of the magnetic
field B in the indentation of the magnet assembly with the Tesla Meter. (Use
tack-shaped magnets to increase the magnitude. Make sure the direction of North
and South poles of the little magnets are the same when putting them on the magnet
assembly.)
Figure 5
2.
Determine the weight of the magnets while no current flowing. Mark this value as
W1.
3.
Set the angle to 0 with the direction of the wire coil approximately parallel to the
o
magnetic field. Set the current to 1.0 A. and the force on the wire should be 0 at the
same time. This is the standard.
4.
o
o
o
o
o
Set the angle to 0 , 30 , 45 , 60 and 90 and determine the new “weight“ of the
5-6
magnet assembly. Mark this value as W2. The difference of W1 and W2 is force.
5.
6.
o
o
o
o
o
Set the angle to 0 , -30 , -45 , -60 and -90 and determine the new “weight“ of the
magnet assembly. Mark this value as W2. The difference of W1 and W2 is force.
Plot the graph of force F versus angle θ and the graph of force F versus Sinθ.
Q7：How could we derive F = iL × B from original Lorentz’s force F = qv × B ?
Q8：Does the force in F = qv × B still work?
Appendix
Length
Length
1st Current Loop PC Board
2nd Current Loop PC Board
3rd Current Loop PC Board
2.2 cm
4.2 cm
3.2 cm
4th Current Loop PC Board
5th Current Loop PC Board
6th Current Loop PC Board
1.2 cm
6.4 cm
8.4 cm
5-7
Unit 6 Oscilloscope
Remark:
1. The rotary switch should be placed in the right position and no any changeover off of
range shall be made during measurement is conducted to prevent damage of the Meter.
2. Turn the Meter off when it is not in use.
3. Disconnect circuit power and discharge all high-voltage capacitors before testing
resistance, continuity, diodes and current.
4. You may press 「AUTO SET」 button when you can't find any stable wave on the
screen. But please do not rely on this button.
Objective
In physic experiments, we usually use some basic instruments to measure the physics
quantities. Measurement of current and voltage are the most common methods. Therefore, in
this experiment, we would like to introduce the application of an oscilloscope.
Apparatus
Oscilloscope, Digital multimeter
Principle
(I) oscilloscope
Electronic equipment can be classified into two categories: analog and digital. Analog
equipment works with continuously variable voltages, while digital equipment works with
discrete binary numbers that represent voltage samples. A conventional phonograph is an
analog device, while a compact disc player is a digital device.
Oscilloscopes can be classified similarly – as analog and digital types. In contrast to an
analog oscilloscope, a digital oscilloscope uses an analog-to-digital converter (ADC) to
convert the measured voltage into digital information. It acquires the waveform as a series of
samples, and stores these samples until it accumulates enough samples to describe a
waveform. The digital oscilloscope then re-assembles the waveform for display on the screen,
as seen in Figure 1
6‐1 Fig. 1
Analog oscilloscopes trace singles, while digital oscilloscopes sample singles and
construct display.
Digital oscilloscopes can be classified into digital storage oscilloscopes (DSOs), digital
phosphor oscilloscopes (DPOs), mixed signal oscilloscopes (MSOs), and digital sampling
oscilloscopes.
The digital approach means that the oscilloscope can display any frequency within its
range with stability, brightness, and clarity. For repetitive signals, the bandwidth of the digital
oscilloscope is a function of the analog bandwidth of the front-end components of the
oscilloscope, commonly referred to as the –3 dB point. For single-shot and transient events,
such as pulses and steps, the bandwidth can be limited by the oscilloscope’s sample rate.
A conventional digital oscilloscope is known as a digital storage oscilloscope (DSO). Its
display typically relies on a raster-type screen rather than the luminous phosphor found in an
older analog oscilloscope.
Digital storage oscilloscopes (DSOs) allow you to capture and view events that may
happen only once – known as transients. Because the waveform information exists in digital
form as a series of stored binary values, it can be analyzed, archived, printed, and otherwise
processed, within the oscilloscope itself or by an external computer. The waveform need not
be continuous; it can be displayed even when the signal disappears. Unlike analog
oscilloscopes, digital storage oscilloscopes provide permanent signal storage and extensive
waveform processing. However, DSOs typically have no real-time intensity grading; therefore,
they cannot express varying levels of intensity in the live signal.
(II)Lissajous figure.
It is instructive to consider the pattern characteristics that result from application of
sine-wave voltages to the vertical and horizontal input terminals. Let us suppose that the
vertical and horizontal deflection voltages are 90∘out of phase with each other. In such case,
6‐2 equal deflection voltages of the same frequency produce a circular pattern, as shown in Fig. 2.
This is a simple example of a Lissajous figure.
Fig. 2
Production of a circular sweep by two sine waves of equal frequency and
amplitude but 90∘out of phase.
If the vertical deflection voltage is unequal to horizontal deflection voltage, a vertical or
horizontal ellipse is displayed, as depicted in Fig. 3. The reason for formation of an ellipse
follows from a comparison of Fig. 3 with Fig 2.In the limit (when one of the deflection
voltages is zero), the pattern collapses into a vertical or a horizontal line.
(a) Fig. 3
(b) Horizontal and vertical deflection frequencies equal.(a) vertical voltage
greater than horizontal voltage; (b) horizontal voltage greater than vertical voltage.
6‐3 Returning to the case of equal deflection voltages of the same frequency, let us observe
the result of varying the phase between the two voltages. As seen in Fig. 4, progressive phase
variation causes the pattern to vary from a straight diagonal line through diagonal ellipses of
different eccentricities to a circle, and then through another series of ellipses to a straight
diagonal line once more.
Fig 4. Lissajous patterns indicating phase difference between sine waves of same frequency and amplitude. When voltages having different frequencies are applied to the vertical and horizontal
deflection plates, crossover types of Lissajous figures are produced. For example, Fig. 5
6‐4 shows the range of patterns that are formed by deflection voltages having a 1:2 frequency
ratio, and with various phase differences between them. This is commonly called a “bow-tie”
pattern. Note that if the deflection frequencies are almost but not quite in exact 1:2 ratio, the
pattern will “writhe” on the screen as it goes through the progressive phases illustrated in Fig.
5. Lissajous patterns are widely used to check the calibration of a generator against a
frequency standard at various harmonic intervals.
Fig. 5
Lissajous patterns for 1:2 frequency ratio
To obtain the ratio of vertical and horizontal deflection frequencies from any Lissajous
pattern, count the number of horizontal tangent points, and divide this number by the number
of vertical tangent points. Note that this method is straightforward so long as the pattern
contains visible crossovers. However, in the example of Fig. 5C, the crossover is masked by
6‐5 trace coincidence; that is, the two horizontal tangent points fall together in this special case of
phase relations. The beginning scope technician must be on guard in such situations to avoid
jumping to false conclusions.
Oscilloscopes can be used in the X-Y mode to determine the phase angle between two
singles of the same frequency. The pattern displayed on the screen may vary from a straight
line with a positive slope, if the singles are in phase, to a straight line with a negative slope for
singles 180∘out of phase, as shown in Fig. 6.
Fig.6 Lissajous patterns for selected phase angles.
If the phase angle is any angle between 0∘ and 360∘besides 180∘, a circle or an
ellipse, as shown in Fig. 7, will be displayed. The phase angle is easily determine from the
ellipse. The ratio of the Y-axis intercept, represented as Y1 in Fig. 7, and the maximum vertical
deflection, Y2, is equal to the sine of the phase angle; that is,
Y
Sinθ = 1
Y2
6‐6 where
θ= phase angle in degrees
Y1 = Y-axis intercept
Y2 = maximum vertical deflection
Fig. 7
Evaluation of phase relationship
Instructions
Read the appendix for Digital Storage Oscilloscope panel before the experiment to
understand the function of the switches, knobs, and connectors and then start to operate it.
(I) Power Up
1.
Disconnect all the probes and turn the power on. Digital Storage Oscilloscope
2.
3.
4.
5.
6.
would run the power-up tests. When the testing is done, power up procedure is
finished.
Press “CH1 MENU” button to switch CH1 on.
Adjust the “HORIZONTAL” knob to set the horizontal position to 0.
Adjust the “VERTICAL” knob to set the vertical position to 0.
Adjust “Volts/div” knob of CH1 to the maximum, i.e., 5 Volts/div.
Press “TRIG MENU” button to enter trigger menu.
7.
Press the Type to select "Edge", Source to select "CH1", Slope to select "Rising",
Mode to select "Auto" and Coupling to select "AC".
8. Press “CH1 MENU” button back to CH1 menu.
9. Connect the CH1 to Function Generator.
10. If the wave on the screen is unstable, adjust “Trigger level” probe to make the wave
stable. (The trigger level is usually set to 0V.)
Q1：If trigger level is larger than the maximum amplitude of trigger source, what would
you observe?
11. If the amplitude of the wave on the screen is too large or too small, rotate the
“Volts/div” knob until the wave occupies 70％ of the screen.
6‐7 12. If the wave is too dense or too sparse, rotate the “Sec/div” knob until there is 1~2
complete waves.
(II) AC voltage Measurement
1.
2.
Count the number of vertical grids from the highest peak to the lowest point of the
wave.
Peak-to-peak voltage V P − P = ( the number of vertical grids that peak-to-trough
3.
voltage of the wave occupies)×(Volts/div).
Calculate the amplitude Vm of the wave.
4.
Press “CURSOR” to enter CURSOR menu. The light of cursor1、cursor2 on the
panel shall be on.
5.
6.
Press Type to select "Voltage" and Source to select "CH1".
Rotate the “HORIZONTAL” knob of CH1、CH2 separately. Make the two cursors
7.
on the screen be the same level with the peak and the tough of the wave.
Read the delta voltage in the Cursor Menu, which is the peak-to-peak voltage of the
wave.
8.
9.
Press “MEASURE” to enter Measure menu.
Press the option button on the top to enter Measure 1 Menu.
10. Press Source to select “CH1” and Type to select "PK-PK".
11. Press Back to Measure menu.
12. Read the peak-to-peak amplitude of the wave V P − P .
13. Use the Multimeter to measure Vrms of the voltage. Use the following equation to
calculate Vm
Vm = Vrms × 2
14. Compare the results of step 3、7、12、13.
15. Press “CH1 MENU” back to CH1 menu.
16. Press Coupling to select "DC".
17. Adjust the DC Offset Control of the function generator. Observe the wave changes.
18. Press Coupling to select "AC". Observe the wave changes and compare them with
step 7.
Q2：What's the difference between DC coupling and AC coupling?
(III) Frequency measurement
1. The same as step (I) without rebooting the oscilloscope.
2. Count the number of horizontal grids of one period.
6‐8 3.
Period T=（number of horizontal grids of one period）×（SEC/DIV）.
4.
Calculate the frequency.
5.
Press “CURSOR” to enter CURSOR menu. The light of cursor1、cursor2 on the
panel shall be on.
6.
7.
Press Type to select "Time" and Source to select "CH1".
Rotate the “HORIZONTAL” knobs of CH1、CH2 separately. Make the two cursors
8.
on the screen on the two consequent peaks.
Read the delta time in the Cursor Menu, which is the period. Calculate the
frequency.
9. Press “MEASURE” to enter Measure menu.
10. Press the option button on the top to enter Measure 1 Menu.
11.
12.
13.
14.
Press Source to select “CH1” and Type to select "Freq".
Press Back to Measure menu.
Read the frequency.
Compare the results of step 4、8、13.
Q3：Explain the differences of the results in step 4、8、13.
(IV) Lissajous pattern
1.
2.
3.
Press”CH1 MENU” and “CH2 MENU” to switch CH1 and CH2 on.
Adjust “Volts/div”knobs of CH1 and CH2 separately to the maximum, i.e., 5
Volts/div.
Connect the CH1 and CH2 to two Function Generators separately.
4.
5.
6.
Press DISPLAY to enter DISPLAY menu.
Press Format to select "XY".
If the pattern on the screen is too large or too small, rotate the “Volts/div” knobs of
CH1 or CH2 to adjust.
7.
Find several Lissajous patterns (refer to Fig. 8). Draw the patterns and put the
frequencies down.
Find the ratios of the frequencies of two signals from the patterns and compare with
the frequencies you recorded.
8.
6‐9 X= sin (ω1 t)
Y= sin (ω2 t +δ)
0
Phase Shite δ 3π
π
π
4
2
4
π
1：1 2：1 Frequency Ratio 3：1 ω1：ω2 3：2 4：3 5：3 5：4 Fig. 8
Typical Lissajous patterns for a variety of frequency ratios.
(V) Measuring the transmission speed of transmission line
1.
2.
3.
4.
Find two transmission lines. One is 1m in length and the other is 60m.
Connect the signal splitter to the output terminal of the function generator. Connect
two transmission lines to the splitter and CH1, Ch2 separately. (CH1 for 1m
transmission line; CH2 for 60m transmission line.)
Set the output signal to sine wave and the frequency to about 2.2MHz.
Open both CH1 and CH2. Try to find two complete waves. Press the “CURSOR” to
select "Time" Type and "CH1" Source. Place “CURSOR 1” to one peak of CH1.
Place “CURSOR 2”to the consequent peak of CH2. Read the delta time Δt .
5.
Calculate the speed of the transmission line.
6‐10 v=
6.
Δd
Δt
(Please mark the unit.)
Repeat step 3~5 and set the frequencies from about 1 to about 2.2 MHz. Get one
data for each 0.2 MHz, i.e., 5 data totally.
Q4：What is the influence of different frequencies to the speed of the transmission line?
Why do we adopt such high frequency?
Q5：Alan talks to his girlfriend Selena on Net phone. He finds out he always hears echo
of his voice 200msec after his own voice. Assume that the frequency of carrier
wave of the voice signal is 1.8MHz. Please estimate which city is Selena in while
Alan is in NCTU campus ( Hsinchu )?
7.
Find two 60m-long transmission lines and connect them in series. Set the switching
frequencies to 2.2 MHz and repeat step 1~5.
Q6: Is the time difference between the first peak of the CH1 and CH2 signal just the
time lag between these two signals? Explain your answer in detail.
Q7: Do you get the same signal propagation speeds in the different length transmission
lines? If not, explain the reason.
6‐11 A. Digital storage Oscilloscope (TDS 2022 )
The front plane
1.
Display area
Icon display shows acquisition mode.
Sample mode
Peak detect mode
Average mode
6‐12 2.
Trigger status indicates the following:
The oscilloscope is acquiring pretrigger data. All triggers are
ignored in this state.
All pretrigger data has been acquired and the oscilloscope is
ready to accept a trigger.
The oscilloscope has seen a trigger and is acquiring the
posttrigger data.
The oscilloscope has stopped acquiring waveform data.
The oscilloscope has completed a Single Sequence
acquisition.
The oscilloscope is in auto mode and is acquiring waveforms
in the absence of triggers.
The oscilloscope is acquiring and displaying waveform data
continuously in scan mode.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Marker shows horizontal trigger position. Turn the HORIZONTAL POSITION knob to
adjust the position of the marker.
Readout shows the time at the center graticule. The trigger time is zero.
Marker shows Edge or Pulse Width trigger level.
On-screen markers show the ground reference points of the displayed waveforms. If
there is no marker, the channel is not displayed.
An arrow icon indicates that the waveform is inverted.
Readouts show the vertical scale factors of the channels.
A BW icon indicates that the channel is bandwidth limited.
Readout shows main time base setting.
Readout shows window time base setting if it is in use.
Readout shows trigger source used for triggering.
Icon shows selected trigger type as follows:
Edge trigger for the rising edge.
Edge trigger for the falling edge.
Video trigger for line sync.
Video trigger for field sync.
Pulse Width trigger, positive polarity.
Pulse Width trigger, negative polarity.
14. Readout shows Edge or Pulse Width trigger level.
15. Display area shows helpful messages; some messages display for only three seconds.
16. If you recall a saved waveform, readout shows information about the reference
6‐13 waveform, such as RefA 1.00V 500μs.
17. Readout shows date and time.
18. Readout shows trigger frequency.
Vertical Controls
POSITION (CH 1 & CH 2). Positions a waveform vertically.
CH 1 & CH 2 MENU. Displays the Vertical menu selections and toggles the display of
the channel waveform on and off.
VOLTS/DIV (CH 1 & CH 2). Selects vertical scale factors.
MATH MENU. Displays waveform math operations menu and toggles the display of
the math waveform on and off.
6‐14 Horizontal Controls
POSITION. Adjusts the horizontal position of all channel and math waveforms.
The resolution of this control varies with the time base setting.
NOTE. To make a large adjustment to the horizontal position, turn the SEC/DIV knob to
a larger value, change the horizontal position, and then turn the SEC/DIV knob back to
the previous value.
HORIZ MENU. Displays the Horizontal Menu.
SET TO ZERO. Sets the horizontal position to zero.
SEC/DIV. Selects the horizontal time/div (scale factor) for the main or the window time
base. When Window Zone is enabled, it changes the width of the window zone by
changing the window time base.
6‐15 Trigger Controls
LEVEL. When you use an Edge or Pulse trigger, the LEVEL knob sets the amplitude
level that the signal must cross to acquire a waveform.
TRIG MENU. Displays the Trigger Menu.
SET TO 50%. The trigger level is set to the vertical midpoint between the peaks of the
trigger signal.
FORCE TRIG. Completes an acquisition regardless of an adequate trigger signal. This
button has no effect if the acquisition is already stopped.
TRIG VIEW. Displays the trigger waveform in place of the channel waveform while
you hold down the TRIG VIEW button. Use this to see how the trigger settings affect the
trigger signal, such as trigger coupling.
6‐16 Menu and Control Buttons
SAVE/RECALL. Displays the Save/Recall Menu for setups and waveforms.
MEASURE. Displays the automated measurements menu. ACQUIRE. Displays the
Acquire Menu.
DISPLAY. Displays the Display Menu.
CURSOR. Displays the Cursor Menu. Vertical Position controls adjust cursor position
while displaying the Cursor Menu and the cursors are activated. Cursors remain
displayed (unless the Type option is set to Off) after leaving the Cursor Menu but are not
adjustable.
UTILITY. Displays the Utility Menu.
HELP. Displays the Help Menu.
DEFAULT SETUP. Recalls the factory setup.
AUTOSET. Automatically sets the oscilloscope controls to produce a usable display of
the input signals.
SINGLE SEQ. Acquires a single waveform and then stops.
RUN/STOP. Continuously acquires waveforms or stops the acquisition.
PRINT. Starts print operations.
6‐17 B. Synthesized Function Generator (SFG – 1003 function generator)
6‐18 6‐19 6‐20 C. Front panel controls and indicators of DC power supply
(9) (8)
(4) (10) (2) (1) (3)
(7)
(6)
(5)
Fig. 21 GPC－3030D DC power supply
(1)
(2)
(3)
(4)
(5)
C.V. indicator
C.C. indicator
Voltage control
Current control
"十" output terminal
(6)
(7)
(8)
(9)
(10)
"GND" output terminal
"–" output terminal
Voltage meter
Current meter
Power switch
6‐21 Unit 7 RLC Series Circuit
I.
Damped Oscillations
Remark:
1. Make sure that your circuit is not a short circuit before you turn the power on.
Keywords
RLC Circuit, LC Oscillation, Damped Oscillation, Resonance, Simple Harmonic Motion
(SHM), Damped Simple Harmonic Motion, Kirchhoff’s loop rule.
Objective
In this experiment, we construct RLC series circuit to study the damped oscillation.
Apparatus
Oscilloscope, resistor, capacitor, inductor, function generator, connector, and LCR
meter.
Principle
A system can oscillate when it has two ways of storing energy and the energy can flow
alternately from one mode of storage to the other. In an electric circuit which contains an
inductor L and a capacitor C, energy can be stored in the magnetic field of L or in the
electrostatic field C. As the flow of current discharges C, a magnetic field is developed
around L. As the magnetic field decays, the induced voltage causes C to charge with a
polarity opposite to the original one. Then the process reverses. RLC circuit contains not only
L and C but also a resistor R, which dissipates a certain fraction of the energy during each
cycle.
7-1
Resistor R
Inductor L
VR(t)
VL(t)
Function generator
ε(t)
Capacitor C
VC(t)
Oscilloscope
Fig. 1
In the RLC circuit we must provide a way of introducing current and a way of observing
oscillation. In the circuit of Fig. 1, the RLC series circuit is connected to the function
generator, supplying the voltage and current. The oscillation of charge in the loop can be
studied by observing the potential across C with an oscilloscope.
From Kirchhoff's rules, the algebraic sum of the changes in potential around a closed
loop is zero. Therefore, the equation for this RLC circuit is written as
V R (t ) + VL (t ) + VC (t ) = ε (t )
(1)
Where ε(t) is the emf (Electromotive force) supplied by the function generator. VR(t), VL(t)
and VC(t) are the potentials across the resistor, the inductor and the capacitor. We first use the
dQ(t )
to obtain
fact that i (t ) =
dt
dV (t )
dQ(t )
=C C
1. Capacitor characteristic: Q(t ) = VC (t ) ⋅ C => i (t ) =
dt
dt
dVC (t )
⋅ RC
2. Ohm's law: V R (t ) = i (t ) ⋅ R =
dt
3. Inductor characteristic: V L (t ) = L ⋅
d 2VC (t )
di (t )
= LC ⋅
dt
dt 2
Then we can get the second order differential equation.
d 2VC (t ) R dVC (t )
1
ε (t )
+ ⋅
+
⋅ VC (t ) =
2
L
dt
LC
LC
dt
(2)
The solution of Eq. 2 depends on ε(t), the emf supplied by the function generator. We
will study this circuit in two ways. In this section, we provide a square wave of low frequency.
In next section, we will discuss the case of inputting a sinusoidal signal.
7-2
ε(t)
ε0
OA
B
t
Fig. 2
The function generator generates a square wave of low frequency, as shown in Fig. 2.
Each time the square wave jumps from + to – or – to +, the change in current sets RLC circuit
into oscillation. At point A, ε(t) jumps from -ε0 to ε0. Capacitor is being charged until it is
fully charged. At point B, ε(t) jumps from ε0 to -ε0. Capacitor is discharging and then it is
reversely charged with a polarity opposite to the original one. In the following, we discuss
these two processes separately:
(a) Charging process: ε(t) = ε0, the 2nd order differential equation can be represented as:
d 2VC (t ) R dVC (t )
ε
1
+ ⋅
+
⋅ VC (t ) = 0
2
L
dt
LC
LC
dt
(3)
Consider the initial condition: VC (t = 0) = −ε 0 . The solution of Eq. 3 is
Oscillation term
Amplitude term
V c ( t ) = ε 0 (1 − 2 1 + (
where β =
R
, ω=
2L
β 2 −β t
) e
cos (ω t − φ ))
ω
(4)
β
1
R
− ( ) 2 , φ = tan −1 . β and ω depend on R, L, and C.
ω
LC
2L
(b) Reverse charging process: ε(t) = - ε0, the 2nd order differential equation can be
represented as:
ε
d 2VC (t ) R dVC (t ) 1
VC (t ) = − 0
+
+
2
L dt
LC
LC
dt
7-3
Consider the initial condition: VC (t = 0) = ε 0 . The solution is:
V c (t ) = 2ε 0
1+ (
β 2 −β t
) e
cos ( ω t + φ )) − ε 0
ω
(5)
Eq. 4 and Eq. 5 describe the damped oscillations in RLC circuit.
VC(t)
ε(t)
We can see that the amplitude terms of both Eq. 4 and Eq. 5 have the common factor
e − β t . And the oscillation terms have the common factor cos(ωt). That is, the value of the
charge on the capacitor undergoes a damped harmonic oscillation in analogy with a
mass–spring system moving in a viscous medium. The behavior of RLC circuit is shown as
below:
2
1
⎛ R⎞
(1) When ⎜ ⎟ >
, ω is an imaginary number and cos(ωt) = cosh(jωt) , which is a
⎝ 2L⎠
LC
hyperbolic cosine function. There is no oscillation. It's said to be "over damped".
2
1
⎛ R⎞
(2) When ⎜ ⎟ =
, ω = 0 and cos(ωt) = 1. There is no oscillation, either. It's said to be
⎝ 2L⎠
LC
"critical damped".
2
1
⎛ R⎞
(3) When ⎜ ⎟ <
, ω is a real number. Oscillation occurs. It's said to be "under
⎝ 2L⎠
LC
2
1
⎛ R ⎞
damped". If ⎜ ⎟ ⟨⟨
, the angular frequency of the oscillation would approach
⎝ 2 L ⎠ LC
ω0 =
1
, called nature angular frequency.
LC
In Reverse charging process, the graphs of VC(t) versus time for these three cases are shown
7-4
in Fig. 3.
Fig. 3
Instructions
1. Firstly, make sure that the function generator and the oscilloscope are off. Construct the
circuit in Fig. 1, in which R=100Ω, L=10mH, C=0.01μF. Turn on the function generator
and the oscilloscope. Set the generator to produce a square wave and set the frequency to
500Hz. Display the voltage across the capacitor and the output signal of the function
generator on the oscilloscope with Channel 1 and 2, respectively. Adjust the scope
controls to obtain steady patterns.
2. Set the generator output amplitude control to 1V. Observe the signal of the scope CH1.
Can you observe the “under damped oscillation” pattern? If not, adjust the scope controls
or check the circuit.
Q1: Given that C=0.01μF and L=10mH (or C=100pF and L=10mH), what is the values of
R if you would observe the under damped oscillation?
3. Observe that the oscillatory amplitude decays with time in one (reverse) charging process.
Measure the amplitude and plot a graph of amplitude versus time. Determine the
experimental time constant β and compare it with the value predicted by the relation
R
β=
.
2L
4. Without making any adjustments to the functional generator, repeat Step 3 with R=100Ω,
L=10mH, C=0.01μF.
Q2: Compare the envelope of the oscillatory curve in Step 3 with one in Step 4. Which
one is better consistent with the exponential factor in Eq. 5 (or Eq. 4)? Explain
7-5
Why?
5. Find the damped frequency f (or period T), and calculate the damped angular frequency
2π
). Compare it with the value predicted by the relation
ω = 2π ⋅ f (or ω =
T
1
R
− ( )2 .
ω=
LC
2L
6. Keep the resistance R and the inductance L constant. Repeat Step 5 to find the angular
frequency for various capacitances. (At least 5 different capacitances.) It is suggested that
the capacitance should be between 0.002μF and 0.04μF. Plot the graph of ω2 vs. 1/C. Eq.
4 predicts that ω2 should be proportional to 1/C. Find an equation to represent the data
and compare it with the prediction.
7. Keep the inductance and the capacitance constant. Vary the resistance; observe the
critical damped and over damped oscillation? Explain what difference between the
critical damped and over damped oscillation. And record the resistance R for the critical
damped oscillation.
Q3: Please find some applications of damped oscillation in daily life.
7-6
II. Forced Oscillations
Remark:
1. Make sure that your circuit is not a short circuit before you turn the power on.
Keywords
RLC Circuit, LC Oscillation, Forced Oscillation, Resonance, Simple Harmonic Motion
(SHM), Kirchhoff’s loop rule.
Objective
In this experiment, we study the frequency response of RLC circuit excited by a
sinusoidal signal.
Apparatus
Oscilloscope, resistor, capacitor, inductor, function generator, connector, and LCR
meter.
Principle
In Part I, we have studied the damped oscillations. In that case, the generator supplies a
square wave. In this experiment, we would study RLC circuit which is driven by a sinusoidal
wave generator. The input signal ε (t ) is shown as Fig. 5. The emf ε (t ) is written as
ε (t ) = ε 0 cos(ω ⋅ t )
Where ω = 2π ⋅ f is the angular frequency in rad/s and f is the frequency in hertz (Hz). ε 0
is the peak emf of the ac source.
L
VL(t)
R
VR(t)
Function generator ε(t)
C
Fig. 4
7-7
VC(t)
Oscilloscope
ε(t)
O
t
Fig. 5
From Eq. 2, we can get
d 2VC (t ) R dVC (t ) 1
ε
+ ⋅
+
⋅ VC (t ) = 0 cos(ω ⋅ t )
2
L
dt
LC
LC
dt
(6)
The voltage across R is
Amplitude term
Oscillation term
VR (t ) =
φ = tan −1
ε0R
1 2
R 2 + (ωL −
)
ωC
ωL −
⋅ cos(ω ⋅ t − φ )
(7)
1
ωC
R
The amplitude of VR depends on the frequency. A graph of amplitude as a function of
frequency will look like curve in Fig. 6. The amplitude of VR reaches a maximum value ε 0 ,
1
. This condition defines the resonance angular frequency
when ωL =
ωC
ω0 =
1
LC
This is the same with the natural angular frequency (see Part I).
Q4: According to Eq. 7, VR (t ) = ε 0 cos(ωt ) when ω = ω 0 . By Kirchhoff's rules, at
resonance, how are the amplitude of VL(t) and VC(t) related, and what is the phase
7-8
relation between VL(t) and VC(t)?
The amplitude of VR decreases to
ε0
2
at the cutoff frequencies ω l and ω h , as shown
in Fig. 6. A bandwidth, a half-width of frequency, is defined as
Δω = ω h − ω l
For RLC series circuit,
Δω =
R
L
It is independent on the capacitance C. Moreover, the resonance angular frequency depends
on L and C. The characteristics of RLC circuit vary with the resistance, inductance and
capacitance.
|VR|
ε0
ε0
2
ωl ω0 ωh
ω
Fig. 6
Q5: Prove the bandwidth is equal to
R
for RLC series circuit excited by a sinusoidal
L
signal.
Instructions
1.
2.
Construct the circuit in Fig. 4, in which R=400Ω, L=10mH, C=0.001μF.
Turn on the function generator and the oscilloscope. Set the generator to produce a sine
wave with an amplitude of 1V. (Make sure that “OFFSET switch” is at OFF position.)
7-9
Display the voltage across the resistor, VR(t), and the output signal of the function
generator, ε (t ) , on the oscilloscope with Channel 1 and 2, respectively.
3.
Adjust the frequency until the amplitude of VR reaches the maximum value. Then record
the frequency. It is the resonance frequency. Compare this frequency with the prediction
1
of the relation ω 0 =
. Moreover, record the maximum amplitude of VR and
LC
compare it with the theoretical value ε 0 . Determine the phase angle of VR with respect to
ε (t ) at the resonance frequency. Again, compare it with the theoretical value.
4.
Measure the amplitude of VR as a function of f. Plot a graph of VR as a function of f. Be
sure to make enough measurements to locate accurately the frequencies at which |VR| is
ε0
2
5.
so that the bandwidth can be determined.
Adjust the frequency to the experimental resonance frequency. Then, set the scope in XY
mode to observe the Lissajous figure of VR and the inputting sine wave at different
frequencies.
Q6: Explain how does the phase relation between VR and ε (t ) depend on frequencies,
according to the result of Step 5. Dose it consist with the prediction of Eq. 7?
6.
Set the scope in YT mode. Then adjust the frequency to the experimental resonance
frequency. Measure the voltage across the inductor |VL| and the voltage across the
capacitor |VC| at the experimental resonance frequency.
Q7: In Step 6, the experimental values of |VL| and |VC| should be bigger than ε 0 . Would
it violate the energy conservation? Does it violate Kirchhoff’s loop rule?
7.
8.
Keep the inductance L and the capacitance C constant. Vary the resistance, and repeat
Step 1~4.
Keep the resistance R and the inductance L constant. Vary the capacitance, and repeat
Step 1~4.
Q8: How do the characteristics of the curves in Step 7 and Step 8 vary with the
capacitance and the resistance?
Q9: If we keep the resistance R and the capacitance C constant in Step 7, and vary the
inductance, how do the characteristics of the curve vary with the inductance?
Q10：What is “Bandpass Filter”? Find some applications of bandpass filters in daily life.
7-10
Appendix : Forced Oscillation:
C
L
A.C
ε(t)
VR(t)
R
The above figure shows an ac circuit consisting of a capacitor, a inductor and a resistor
connected in series across the terminals of an ac generator. The applied voltage is given by
ε (t ) = ε 0 ⋅ cos(ω ⋅ t ) . The current of the circuit is i(t ) . Kirchhoff’s loop rule applied to this
circuit gives
ε (t ) = ε 0 ⋅ cos(ω ⋅ t ) = i(t ) R + L
d
1
i (t ) + ∫ i (t )dt
dt
C
where R, L and C are the resistance, the inductance, and the capacitance. The impedance Z of
the circuit is
Z = R + jωL +
1
（where j ≡ − 1 ）
jωC
According to the ohm's law, we can get the effective current I of the circuit:
I =
=
ε 0 e jwt
Z
ε 0 e jwt
=
R + jω L +
ε0
Where φ = tan
jω C
R + j (ω L −
1
)
ωC
⋅ e j ( wt −φ )
1 2
R 2 + (ω L −
)
ωC
−1
1
ε 0 e jwt
=
1
ωL −
ωC
R
Get i (t ) by taking the real part of I
i (t ) = Re[ I ] =
ε0
1 2
R 2 + (ωL −
)
ωC
⋅ cos(ω ⋅ t − φ )
7-11
=
ε 0 e jwt
R 2 + (ω L −
1
ωC
) 2 ⋅ e jφ
Thus, the output voltage VR(t) is
VR (t ) = i (t ) R =
ε0R
1 2
R + (ωL −
)
ωC
⋅ cos(ω ⋅ t − φ )
2
7-12
Unit 8 Hall Effect
Remarks:
1.
2.
7.
The current cannot exceed 50mA.
Be careful to utilize the n-type & p-type germanium Hall effect wafers and avoid
impact.
Do not disassemble the magnetic assembly. And keep your own atmcard away from the
magnetic assembly, or the magnetic stripe may be damaged.
Slowly adjust the current and voltage control. Because sudden pulse may damage the
apparatus.
The probe of the Tesla meter is fragile and expensive. Use it carefully.
Before turning on the Tesla meter, install the sensor probe first. Make sure the probe is
properly installed.
The Tesla meter should be zeroed by a zero flux chamber before use.
8.
Conversion of the magnetic field: 1 Gauss＝ 10 −4 T
9.
The density of the carriers for intrinsic germanium is around 2.4 ×10 −13 cm −3 .
3.
4.
5.
6.
Keywords
Hall Effect, Magnetic Field, Lorentz Force
Objectives Investigate the deflection of the carriers in the conductor caused by the Lorentz force due
to the applied magnetic field. We can also conclude whether positive or negative the carriers
are by the measurement of this experiment.
Apparatus N-type & P-type germanium Hall Effect wafers, Microvoltmeter, Magnetic assembly,
Power supply (contains two outputs), Digital voltmeter, Wires
8-1
Microvoltmeter
Power supply
Magnetic
assembly
Hall Effect
wafers
Digital voltmeter
Fig.1 Apparatus
Fig.2 Hall Effect wafers
8-2
Principles When a electric charge q moving through a uniform magnetic field with speed , it
would be affected by a magnetic force
. The force is perpendicular to both and ,
and have its maximum when is perpendicular to .
Hall (Edwin Hall 1855-1938) brought an interesting question: Would the current in the
conductor be deflected by a magnetic field? He expected the resistance would increase
because of the magnetic field force the current gathered mostly in one side of the conductor
result in the smaller effective area of the cross-section for the current. This thought is good,
although, the sensitivity of his apparatus wasn't good enough to measure this change of the
resistance. Then he improved his idea: Since the current deflects, there should be a stress in
the lateral side. Henry Rowland, Hall's advisor, had once measured that there was a tiny
potential difference in the lateral side (the y axis) of the conductor; therefore, he suggested
Hall to repeat the experiment. Finally, in October, 1879, Hall successfully measured the
lateral potential difference by using a thin gold foil. This is the famous Hall Effect.
z
B
y
P
w
Id
A
t
x
O
Fig.3 the diagram of Hall Effect (the carriers are positive charges)
The design of Hall Effect experiment is shown in figure 3. In the conductor, a uniform
goes along the x-axis. The density of the current is
/ , where
is
current
the area of the cross-section of the conductor, w is the width, and t is the thickness. Suppose
there is only one kind of carriers in the conductor and the charge of the carrier is e (For
convenience in discussion, we assume it as a positive charge first i.e.
the current:
⁄
0.) The density of
(1)
is the drift velocity of the carriers along
where n is the density of the carriers,
the x axis.
When no magnetic field is applied, there would be no potential difference in the lateral
side. (i.e. no potential difference between point O and point P in Fig.3.) Once a uniformly
distributed magnetic field
̂ is applied, the carriers deflect towards
direction due to
the magnetic force and cause the accumulated positive charges at the side of point O. At the
same time, because the conductor is neutral, the corresponding negative charges would
accumulate at the side of point P, and induce a lateral electric field along
direction. Then
the carriers on the conductor are affected by both magnetic field and induced electric field.
8-3
Finally, when the electric force due to the lateral electric field
the magnetic force:
is strong enough to balance
(2)
The potential difference between point O and point P, at this moment, is fixed and
. This is so called Hall potential difference. If we substitute equation (1) into
we find:
,
(3)
Equation (3) represents the linear relation between
and
(and B). We can compute
the density of the carriers from the slope. Besides, from the sign of
we can know whether
the nature of carriers is positive or negative. Something is worth to emphasize is that the
relationship between
and the thickness t is an inverse ratio. Therefore, the key point of
Hall’s succeed is that he utilized the thin gold foil.
In an ideal condition, if we want to measure , we just connect the microvoltmeter with
point O and P in Fig.3. But if we find that
is nonzero when there is no magnetic field,in
order to have correctness, we should have a fine tuning design to solve this problem.
Q1: What is possible reason that the nonideal condition occurs?
The fine tuning design in the experiment is the fine tuning voltage divider (Fig. 4). In the
procedure of regulation, we can tune the microvoltmeter reading to be zero by adjusting the
fine tuning voltage divider.
Q2: Can you figure out the principle of the fine tuning voltage divider?
Id
The fine tuning voltage divider
Id
Fig.4 N-type & P-type germanium Hall effect wafers
8-4
Instructions 1.
2.
3.
4.
Set range: Set the operation range of the apparatuses before connecting any wires. The
microvoltmeter is around 30mV; the current sent to n-type & p-type germanium Hall
effect wafers is around 1~50mA, and the magnetic field is around 1k~4kG.
Zero process: Before connecting any wires, take the zeroing process for the
microvoltmeter.
Connect wires: Connect the wires with the n-type germanium Hall effect wafer (Fig. 1),
and notice that don’t turn on the power before you check on it. Because the current
output from the power supply changes violent. You must check the circuit again and
again. Make sure before we turn on the power.
Measurement:
A. Record the current . Make sure the magnetic field is zero at this moment.
B. Check if the microvoltmeter reading is zero or not. If not, adjust the fine tuning
voltage divider and tune the microvoltmeter reading to be zero.
C. Vary the intensity of the magnetic field by adjusting the distance between two
magnets. (Make sure that the wafer is able to put in between them.) Measure the
magnetic field by the Tesla Meter and record it. (The manual of the Tesla Meter is in
the appendix of Unit 5-Current Balance.)
D.
E.
F.
G.
H.
5.
Record the Hall potential difference
and the sign of carriers.
Fix the current
of the sample, vary 5 different magnetic field (between
1kG~4kG) and record the Hall potential difference
respectively.
Plot the figure of
versus B and calculate the density of the carriers n.
Keep the magnetic field B fixed, vary 5 different current
and record the Hall
potential difference
respectively.
Plot the figure of B versus
and calculate the density of carriers n.
Utilize p-type germanium Hall effect wafers:
Utilize another germanium Hall Effect wafers and repeat step 3~4.
Q3: What is the application of the Hall Effect?
Q4: What is the reason of Hall succeed in this experiment by utilize the thin gold foil?
And, why the sample we utilize now isn't necessarily thin?
Q5: Based on your experimental result, what is difference between n-type & p-type
germanium Hall effect wafers?
Q6: Is the sign of the carriers whether positive or negative significant? Is there any
underlying meaning?
8-5
Unit 9 Interference and Diffraction
Remarks:
1.
2.
3.
Please note that laser radiation is harmful. Do not stare into beam.
Do not bend over the table during the experiment. Since your eyes may exposed
around laser beam.
Make sure your laser beam won’t hurt anyone else. When you are moving a laser,
please block the beam or turn it off first.
Keywords
Tomas Young, Double-slit, Single-slit, Interference, Diffraction, Wave Optics, Wave
Mechanics, Coherence, Spatial Coherence,
Objectives
Young’s double-slit experiment was one of the famous optics experiments in 19 century.
Interference fringes can be seen on the screen far away when light source passes through a
double-slit. The experiment established the theory of "wave optics". It also gave the principle
of qualitative observation of "Wave Mechanics". Therefore, this experiment gives the
opportunity for you to feel the extraordinary of a master by doing the interference and
diffraction experiment.
Apparatus
He-Ne Laser (λ= 6328 Å), Double-slit set, Single-slit set, Optics track, Light sensor,
Rotary motion sensor, SW-750 interface
SW750 interface
He-Ne Laser
Sensor
Optics track
Slits
Fig.1 Experiment set-up
9-1
Principles
(a) Double-slit interference
Y
A
d
θ
S
O
B
E
D
Fig.2 Double-slit interference
The phenomena of interference and diffraction are two remarkable features of the wave
nature of light. Suppose there are two slits A and B as shown in figure 2. When a coherent
light pass through these two slits respectively, there would be a series of bright and dark bands
on a screen called interference fringes. This is the famous Young’s experiment performed in
1802.
For any arbitrary point Y on the screen, the distance between Y and slits are AY and BY
respectively. The optical path difference BE BY AY. If the screen is very far from the slits
(i.e.D d ), the path difference to Y is approximately
. If the path difference is either
zero or some integer multiple of the wavelength, the constructive interference occurs. When
the path difference is an odd multiple of
, the destructive interference occurs.
Constructive interference
Destructive interference
(1)
(2)
The interference fringes on the screen would be symmetric related to the middle point O.
9-2
(b) Single-slit diffraction
Y
A
θ′
W
O
B
D
Fig.3 Single-slit diffraction
When plane waves start to spread into a single-slit, by according to the Huygens’
principle: each point on the approaching wavefronts acts as a source of secondary wavelets.
These wavelets would interfere with each other and form interference fringes due to the
superposition principle. As shown in the figure 3, the width of the slit is W, λ is the
wavelength of light, θ′ is the angle between any arbitrary point Y and the middle point O to
the slit.
Destructive interference
Constructive interference
(3)
(4)
Where n is any integer. The center bright band due to n = 0, with twice width as other
bright bands. Also, the diffraction fringes must be symmetric related to the point O.
In theoretical discussion, we usually assume the width of slits to be extremely small. But
the diffraction of slit itself always happens because of the finite width. Therefore, the fringes
in Young’s double-slit experiment (as shown in Fig.4c) are the combination of interference (as
shown in Fig.4a) and diffraction (as shown in Fig.4b).
9-3
(a)
1
0 . 9
Intensity
0 . 8
0 . 7
0 . 6
0 . 5
0 . 4
0 . 3
0 . 2
0 . 1
0
- 1 5
(b)
- 1 0
- 5
0
5
1 0
1 5
- 1 0
- 5
0
5
1 0
1 5
- 1 0
- 5
0
5
1 0
1 5
0 . 5
0 . 4 5
Intensity
0 . 4
0 . 3 5
0 . 3
0 . 2 5
0 . 2
0 . 1 5
0 . 1
0 . 0 5
0
- 1 5
(c)
0 . 5
0 . 4 5
Intensity
0 . 4
0 . 3 5
0 . 3
0 . 2 5
0 . 2
0 . 1 5
0 . 1
0 . 0 5
0
- 1 5
Center of the screen
（a）Interference effect
（b）Diffraction effect
（c）Combination of both effects
Fig.4 Fringes of double-slit interference
B
C
S
S：Laser
B：Double-slit (or Single-slit)
C：Light sensor
Fig.5
9-4
Instructions
A.
Double-slit interference:
1. Setup the apparatus as shown in figure 5, where S is the laser, B is the double-slit set,
and C is the light sensor. Make sure the rack of light sensor is perpendicular to the
light path.
2. Record the separation of double-slit d. Turn on the laser and adjust the laser and the
double-slit set to get a series of clear and symmetric fringes.
3. Measure the intensity of the fringes by the light sensor.
4. Plot the data in Intensity-Position figure with the computer and analyze the position
of dark fringes
the angle
. Take the distance between the slit and the sensor D to compute
.
5. Substitute θn and the separation of double-slit into equation (2), calculate the
wavelength of the light source.
6. Change another double-slit with different separation and width. Repeat previous
steps.
B.
Single-slit diffraction:
1. The setup is the same as step A. Replace the double-slit with a single-slit.
2. Similar to previous A-2~5, record the width of the slit W. Measure the intensity and
plot with the computer. Compute the angle
’. Finally calculate the wavelength by
equation (3).
3. Change another single-slit and repeat step 1~2.
Questions Q1: What would happen if you use a chromatic light source?
Q2: In previous experiments, if the intensity of the light source is strong enough, can the
number of the fringe be infinite? If not, what would be the constraints? Please
explain it.
Q3: If the double-slit is tilted with a small angle, what would be the fringes?
Q4: If the single-slit is tilted with a small angle, what would be the fringes?
Q5: Is the width of the central bright fringe of the diffraction fringes different to width
of other fringes? Please explain
Q6: There is no laser during the age of Young, how did he do the experiments?
Q7: What is the greatest contribution of Young's interference experiment?
9-5
Unit 10 Millikan's Oil Droplet Experiment
Remarks:
1.
2.
Do not take off the atomizer. Request the teaching assistant to add some oil if you need.
Before turning on any power, make sure you have wired things correctly.
Key words:
Millikan's Oil-Drop Experiment, Electric Field, Terminal velocity (Terminal Speed).
Objective:
We will experimentally determine the unit charge. (1 unit charge = 1.6x10-19 C) Robert A.
Millikan was awarded the Nobel Prize in physics in 1923 for this brilliant experiment.
Apparatus:
Millikan apparatus (microscope with 10x eyepiece and 1.875x objective, oil chamber,
illumination system, oil atomizer, tripod), power supply, CCD camera.
CCD
Microscope
Atomiz
Plate capacitor
Tripod
10-1
Illumination system
Power supply
Principle：
Electricity force
Buoyant force
Oil Droplet
d
Gravity force
The charge carried by an oil droplet can be obtained by analyzing the forces acting on
the oil droplet. Figure 1 shows the forces acting on the droplet when it is rising (or falling)
under the influence of an electric field. Assume that Q is the charge on the spherical droplet
with the mass moil . The forces acting on the droplet are described as following:
(1) Gravity force: moil g
4
mair = π r 3 ρ oil
3
Where r is the radius of the droplet and ρ oil is the oil density.
(2) Buoyant force: mair g
The mass of the air displaced mair is
4
π r 3 ρ air
3
Where r is the radius of the droplet and ρ air is the air density.
mair =
(3) Electricity force： QE
E is the electric potential across the two plates.
With no electric field, the viscous force is balanced by gravity force and buoyant force
acting on the droplet when the droplet reaches a constant velocity. According to Stokes’ Law
the viscous force on a spherical falling body in a viscous medium is given by:
F = 6πrηv
Where η is the coefficient of viscosity and v is the falling velocity. It is convenient to
10-2
define the effective mass and the effective density as
m = moil − mair
ρ = ρ oil − ρ air
Therefore, the terminal velocity of the falling drop is
v=
mg
6π rη
(1)
The mass of the oil droplet is given by
m=
4π r 3
.
3
From Eq. 1, we can get
4
π r 3 ρ g − 6π r η v = 0
3
Thus, the radius of the droplet r is
r=
9ηv
2 ρg
(2)
Hence a measurement of the terminal velocity will enable determination of droplet radius r.
Q1: Derive the terminal velocity.
Q2: Dose the oil droplet quickly reach terminal velocity? Why?
If the droplet is float under the influence of an electric field E, it’s terminal velocity u is
u=
mg − QE
6π rη
(3)
u and v is defined as positive when the droplet is falling. Q may be positive or negative.
The electric field is produced by two parallel plates maintained at a potential difference V and
separated by a distance d. Thus, the electric field E is given by
E=
V
d
10-3
By substituting Eq. 1 into Eq. 3, the charges Q on the droplet is
Q=−
6π rη (u − v)
6π rηd (u − v)
=−
E
V
(4)
Substitute Eq. 2 into Eq. 4. Then we can have the charges Q by the following question
Q=−
6π dη
V
9ηv
(u − v)
2 ρg
(5)
The parameters are shown as following:
η = 1.81× 10−5 Ns
ρ air = 1.29 kg
m3
,
m
2
,
d = 6 × 10−3 m ,
ρ = 874 kg
ρoil = 875.3 kg
m3
,
m3
Substitute these parameters into Eq. 5 and simplify it as following:
Q = −2 × 10 −10
v (u − v )
V
(6)
Therefore, by measuring the velocity of the oil drop under different conditions, the
charge carried by an oil droplet can be determined.
After determining the charges of plenty oil droplets, we make a plot of the number of
times a value of Q occurred vs. Q., The quantization of electric charges can be recognized
from the fact that these charges of all oil droplets are grouping around integer multiples of
elementary charge e. ( e = 16021
× 10 −19 C).
.
Instructions:
A. Preparation:
1. Set up the Millikan apparatus. Plug in the electricity, turn the power on and provide the
illumination.
2. Press the atomizer to spray oil droplets into the chamber. Focus the microscope and get
a clear image of oil droplets.
Q3: In the above step, what direction do the oil droplets move towards in the view of
the microscope? Why?
10-4
3.
4.
5.
6.
Set up CCD camera and adjust the horizontal position.
Close the microscope eyepiece with the CCD camera lens.
Start the software.
Focus the CCD camera and display the image of the droplets and the scale on the
monitor as clearly as possible. Make sure that the scale on the microscope is vertical.
B. Recording and analyzing
1. Set the voltage to 600 V and then switch off the voltage.
2. Press the atomizer to spray oil droplets into the chamber. Start to record the image. As
the oil droplets move to the middle view of the image, turn the voltage on and
record the time. As the oil droplets reach the terminal velocity and then pass through
20~25 markings on the microscope scale, stop recoding.
3. Play the video. Choose one droplet without applied voltage, and measure the time
interval t v for the droplet to pass through 10 markings on the microscope scale.
Calculate the distance s by the equation
s=
x
× 10 −3 m
1.875 × 10
Then calculate the falling velocity v
4. Observe the same droplets in the above step. Wait for it to reach the terminal velocity
under the applied voltage, and measure the time interval t u for the droplet to pass
through 10 markings on the microscope scale. Calculate the velocity u under the
applied voltage.
Without
electricity field
Without
v
10 markings
electricity
tv
With
v
10 markings
field
u electricity
field
With
electricity field
u
10 markings
tu
(The droplet moves in the opposite
direction after an electricity field is
applied.)
(The droplet moves in the same
direction after an electricity field is
applied.)
5. Substitute v 、 u into Eq. 6 to get the charge Q on the oil droplet.
6. Reply the vedio to find the charges on another ten oil droplets.
10-5
7. Make a histogram of your results to determine the unit charge. The histogram is a plot
of the number of times a value of Q occurred vs. Q. Your histogram should look
similar to the figure below.
Q4: How to determine that the oil droplet is positively or negatively charged?
8. Repeat Step 1~7 with setting the voltage to 400 V
Q5: Why don't we find the greatest common factor (g.c.f.) to determine the unit charge?
Would it be any problem to find the g.c.f. directly?
15
n
10
5
Q/10-19 C
1
2
3
4
5
6
10-6
7