Imperial College London
Second Year Physics Laboratory
28 September 2015
Charges and Fields
This 2nd year laboratory experiment consists of two parts. In one part you will measure the
magnetic field of the Earth, in the other part you will measure the value of the elementary charge.
The experiment will be conducted over a normal four weeks lab cycle with approximately half of
the time (4 sessions over two weeks) allocated to each part. As the two parts are independent in
terms of experimental work, you may choose the order to conduct them. You should aim to
switch between the two parts after 4 sessions. Note that your equipment is used by a different
group of students (Monday-Tuesday/Thursday-Friday of each week). Do not rely on finding it
exactly as you left it in the previous week.
You are strongly encouraged to make full use of your demonstrators. They will be more than
happy to talk to you and answer your questions, no matter how silly. It is a good idea to discuss
your results with a demonstrator at the end of each section, before moving on, so that any
problems can be identified while your apparatus is still intact.
Exercise
Before beginning the elementary charge experiment you should complete the short exercise given
at the end of the script.
Approved Scheme of Work (Safety)
In the magnetic field experiment, the wire can be hot – do not touch it when a high current is
flowing.
In the elementary charge experiment, do not run the high voltage supply with the cables
disconnected from the capacitor or with the capacitor cover off.
In both experiments you will use a microscope, which may cause eye strain if poorly adjusted.
Focus the microscope on the scale and the object observed, so you can see them both sharp in a
distant field; do not force your eye into near viewing. Adjust illumination to see the scale and
object clearly. Adjust the stool height for comfortable viewing without straining your neck. Swap
with partner every 15–20 minutes (you may need to adjust the focus or the stool). If in doubt, ask
a demonstrator for help with above precautions.
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Part 1: The Magnetic Field of the Earth1
1. Introduction
The Earth generates a magnetic field which to a fair degree approximates the form of the dipole
field produced by a bar magnet. At present the magnetic poles of the field are actually 11 o or so
out of alignment with the rotational poles of the Earth, and are known to wander about quite
significantly over geological timescales. As a result of the intersection of the Earth’s curved
surface with the spatially varying dipole field, there are usually both significant horizontal and
vertical components present. The total field strength is typically on the order of 30–60 mT and
varies according to local geological conditions. It is also slowly varying with time and its
polarity is expected to reverse in a distant future.
The aim of this experiment is to measure the horizontal and vertical components of the Earth’s B
field using deflection of a fine, current carrying wire. Because of the small size of the B field and
experimental limits on the current a fine wire can carry, the deflection is typically a few 100 mm
and a microscope system is needed to observe the wire.
2. Theoretical background
The force on a small section of wire dl in a magnetic field B is given by the cross product of the
current and field:
F = I dl ´ B
(1)
where I is the current through the wire. In the experiment described here a current carrying wire
is held under tension by a small weight (» 20 g) and passes over fixed pulleys at either end. It is
thus deflected in an arc with the maximum deflection at the centre of the wire. Because of
practical current constraints the total force on the wire is rather small. In order to maximise the
deflection, the wire used needs to be very fine (here about 50 mm in diameter) and is thus rather
fragile. By measuring both vertical and horizontal deflections you will be able to measure two
components of the Earth’s field. By rotating the apparatus 90 o a third component can be
measured.
We need to calculate the total deflection at the centre of the current carrying wire. Consider the
situation shown in figure 1. Each small segment of wire is subject to a horizontal force
d F = I B vert d x .
(2)
dx
I
B
dF
Figure 1. Force, current and B field directions with respect to a wire element dx.
Call the tension in the wire T0. We take the centre of the wire to be the origin, x = 0, y = 0.
Figure 2 shows the balance of forces at a position x along the wire. If we assume the deflection is
small, then the total magnetic force from x = 0 to a point x is just the integral of equation 2,
1
Adapted from an undergraduate experiment developed by Dr Ben Sauer while at the University of Sussex.
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Fmag = I Bvert x , pointing in the –y direction. The magnetic force is balanced by the tension at x,
T(x), since the wire is stationary.
T(x)
y
q
T0
I Bvert x
x
x=0
Figure 2. The I × B force on a wire under tension leads to a displacement. The curvature of the
wire has been greatly exaggerated.
Equating the components of the forces gives two equations:
T ( x )sin q = I Bvert x
(3)
T ( x ) cosq = T0 .
(4)
and
Noting that tan q = d y d x , divide eq. 3 by eq. 4 and integrate. You should find that
y=
I Bvert 2
x .
2T0
(5)
The maximum deflection will be in the middle of the wire (at x = 0). Let L be the total length of
the wire, so that one end is at L/2 and the other at –L/2. Substitute this for x in equation 5 to find
the maximum deflection, ymax. This is the y displacement between the centre and the ends of the
wire.
The derivation of the vertical displacement, z, is similar except it depends on the horizontal
component of the field, Bhor, and the force of gravity acting on the wire element, dx, should be
taken into account. Perform this derivation and deduce if you need to know the wire density and
its diameter.
3. Experimental procedure
Be careful:
1. The wire can become hot – do not touch it when a high current is flowing.
2. Avoid kinking or knotting the wire as this can result in a breakage.
You are provided with an aluminium optical rail on which various items can be securely
mounted. Aluminium, plastic or stainless steel components are used where possible to minimise
stray magnetic fields. A fine tungsten wire (»50 mm diameter) is suspended between two
stainless steel pulleys supported by insulated stands. Fly leads are connected to the pulleys to
provide a means of connecting them to a power supply, voltmeter and ammeter. One end of the
wire should be fixed to a screw in the pulley support. A small piece of sticky tape may be helpful
in keeping the wire in place as the wire material is quite springy. The “free” end of the wire
passes over a second pulley » 1 m from the first and is held under tension by a small weight of
mass m in the range of 3–30 g. The tension in the wire is thus given by T0 = mg.
3.1 Stray B field survey. Your experiment is sensitive to rather small magnetic fields and you
should begin by carrying out a simple survey of the 2nd year lab environment. Take compass
reading of the direction of magnetic north at various points in the lab paying particular attention
to areas where this direction appears to change substantially. You should make a simple sketch
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of the magnetic field vector in the horizontal plane of the lab if you find significant variations.
Ensure that you are not working near a strong magnetic anomaly and initially align your optical
rail in an East-West direction in order to maximise deflection of the current carrying wire in the
vertical plane.
3.2. Setting up the rail. Begin by ensuring that your aluminium rail is horizontal. The two wire
supports should then be placed as far apart as possible on the rail to maximise wire length and
thus deflection of at centre of the wire (deflection scales with length as L2). If necessary, vary the
heights of the support pulleys to ensure that the wire will lie in the horizontal plane when held
under tension over the pulleys. The wire should be surrounded by a plastic tube to avoid
accidental breakage (the wire can be difficult to see from more than a few inches away) or singed
fingers when running at high currents.
3.3. Replacing the wire. The wire you will be using is extremely fine and thus rather fragile. If
you need to replace it use the following method. Cut off several small (»1 cm2) pieces of sticky
tape for later use and tack them to the edge of the table in easy reach. Remove the microscope
and remains of the old wire. Wind up the old wire in a tight loop and put some sticky tape over it
to stop it springing invisibly out of the waste bin, snaring unsuspecting passers by. Unwind a
small length of new wire from the reel taking care not to let it kink. Wrap a few turns round the
fixing pin on one pulley support and add a small piece of sticky tape to hold the free end against
the support rod. Spool out more wire, keeping it as straight as possible and run this into the slot
in the plastic pipe leaving 10 cm or so excess wire beyond the second pulley. Snip the wire with
a pair of scissors while holding both of the cut ends (this requires three hands). Fix the free end
of the wire remaining on the spool down to the end (not the side) of the spool with some tape.
Hold the wire attached to the experiment slightly taught and wrap a few turns round the
tensioning weight hook – again fixing it down with a little tape. Make sure you do this at a point
on the wire that will allow the tensioning weight to hang freely in space once the wire is
supported by the second pulley. Lay the wire over the second pulley and allow the weight to
hang free, placing the wire under tension. Finally reassemble the microscope system.
3.4. Circuit set up. You will need a power supply to control the current, and an ammeter and
voltmeter to monitor the current through the wire and voltage across it. The power supply can
stabilise either the voltage or the current. Wire your circuit and investigate the two modes of
operation. Which one is more suitable to do the experiment?
3.5. Microscope system. You will need to measure deflection of the centre of the wire in both
the vertical and horizontal directions. Ensure that your microscope can view the centre of the
wire from either horizontal or vertical angles of view and that you can bring the wire into sharp
focus. Align the microscope scale such that it is perpendicular to the wire. You may need to
arrange ambient lighting to ensure that both the wire and scale are easily visible at the same time.
Note that when you apply a current to the wire it will move in both the horizontal and vertical
directions and so you may find that the wire moves slightly out of focus when being deflected
across the field of view. Ensure that you know how the microscope scale translates to measured
deflection in suitable units. You can check this against the known diameter of the wire or,
ideally, against a well-calibrated test slide.
3.6. Wire deflection measurements. This experiment is subject to a number of sources of
external noise which make the acquisition of a useful data set more difficult that you might first
imagine. For this reason it is essential that you carry out preliminary measurements (i.e. quick
but sufficiently accurate to discern the wire deflection) in the horizontal and vertical planes and
plot and analyse these data sets fully to understand what the experiment is actually doing, rather
than what the above, idealised theory suggests it might do.
Begin by measuring multiple deflections of the centre point of the wire in the horizontal plane for
a range of currents between 0 and the maximum the power supply can source (~330 mA). Be
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sure to note the direction of the current and the wire movement in order to determine the sign of
the Earth’s field. Reverse the connections to the wire such that it should be deflected in the
opposite direction and repeat your measurements. When looking through the microscope you
may also note a shift of the wire along its length as it heats up and expands at high currents. You
can use this to estimate the temperature of the wire as a function of current, knowing that the
thermal expansion coefficient for tungsten is 4.59×10 –6 /K.
Once you have acquired data for the horizontal displacement of the wire, move the microscope
system to allow you to view deflections in the vertical plane. You should be able to determine
the horizontal components of the Earth’s field by repeating the measurements of the vertical
component. Warning: motion in the vertical plane may be subject to influences other than the B
field – you will need to account for this in the experiment. Look carefully at the effect of current
reversal on the direction of the wire motion in the vertical plane as this can give an important
insight into the experiment. You may find that you need to adjust the tensioning mass in order to
carry out a useful measurement of the vertical displacement. Think in advance how to analyse
the data you are collecting.
4. Data analysis
A plot of ymax vs. current should have a slope which is a simple function of B. This is one way to
determine the field component for a given experimental configuration. You could also solve for
B in terms of your measured quantities and take the weighted mean of all of your data. Whatever
you chose to do, your analysis should produce a magnitude and direction for the vertical and
horizontal components of the Earth’s field, with carefully considered uncertainties. This should
be compared with reference values for the magnitude and direction – the sources of which should
be fully referenced in your report.
Note that the deflection of the wire from the B×I force alone should to first order be linear in
current I and reverse direction if the current also changes direction. However the current can
heat up the wire causing it to expand and possibly sag. A resistive heating effect would probably
scale with I in a different way than the B×I force does. Note also that a thermal effect would
always cause the wire to move in the same direction in the vertical plane, whereas a B field effect
would change direction if the current direction is reversed. Devise a method to measure the
effect due to the magnetic field in the presence of the wire sag.
5. Report
In the report describe what you have learned and achieved. New insights are particularly
valuable. Adhere to the format described in the separate document you were given at the
beginning of the course. Unless told otherwise, write equal amount about this and the other
experiment.
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Imperial College London
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Part 2: Determination of the Elementary Charge
Using Millikan’s Oil Droplet Experiment
1. Introduction
In the early 1900’s a number of laboratories were engaged in experimental efforts to measure the
charge on the electron. Earlier work by J J Thompson at the Clarendon Lab in Cambridge had
suggested the existence of a light carrier of negative charge. In 1909 Robert Millikan provided a
clear demonstration of the quantized nature of electric charge and a robust experimental
determination of the smallest unit of charge with his famous oil droplet experiment. He was later
to be awarded the Nobel Prize for this work in 1923. Millikan’s experiment equated electrostatic
and gravitational forces on a small, charged droplet. Originally water droplets were used, but
these were found to evaporate too fast and were replaced by oil droplets in later work. In essence
the experiment is extremely simple. A charged droplet is introduced into a uniform electric field
produced within a parallel plate capacitor. By carefully varying the voltage applied to the
capacitor a droplet falling under gravity can experience an upward force equal and opposite to
gravity and will come to rest. The Coulomb force on the droplet can then be found, and from this
the charge calculated.
The mass of the droplet in a Millikan style experiment needs to be accurately known in order to
determine the gravitational force it experiences, and the droplets used in these experiments are
typically a few 10’s of micrometers in size. This introduces an experimental complication as
such small objects are extremely difficult to “weigh” directly. Instead fluid dynamic forces on a
freely falling droplet at terminal velocity can be used to determine its mass. The experiment thus
involves creating, charging and trapping droplets electrostatically, together with measurements of
their terminal velocity.
Before beginning the practical part of the experiment you should
complete the short exercise given at the end of the script.
2. Overview of experimental apparatus
The apparatus provided consists of an air spaced parallel plate capacitor, high voltage source,
light source, and simple microscope system. The capacitor is surrounded by a Perspex shield to
minimise air currents, and a mist of fine oil droplets can be introduced into the capacitor using a
so called nebulizer or “perfume spray” system. Typically some small percentage of the droplets
produced will acquire a charge imbalance of ± one or more electrons as they are produced. The
microscope system contains a calibrated graticule against which to measure droplet position but it
does not have sufficient magnification to measure the droplet diameter directly.
A little practice is required to produce and trap droplets. You should ensure that droplets
illuminated by the light source are at best focus and appearing as well defined bright specs in the
microscope field of view. You should also ensure that both droplets and the microscope scale are
clearly visible by suitable set up of droplet and ambient illumination. Before beginning detailed
measurements on a given droplet ensure that it really is a droplet rather than a spec of dust in the
imaging system. It should fall under zero field conditions and rise under high field conditions
allowing you to make multiple measurements on a single droplet.
Warning: Do not run the high voltage supply with the cables
disconnected from the capacitor or with the capacitor cover off.
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3. Theoretical background
3.1. Measurement of the charge on a single oil droplet. Two types of measurement are
required for each charged droplet: one as it moves freely in air with zero field, and one with an
applied electric field. For each droplet you should obtain multiple measurements of:
(a)
(b)
(c)
the terminal velocity at free fall under gravity vg,
the terminal velocity vE of the same droplet as it rises under the combined influence of
gravity and an oppositely directed electric field E.
the voltage V0 required to exactly cancel gravity and bring the droplet to rest.
The terminal velocity depends upon the viscous drag of the air. If we assume that Stokes law
holds, this drag is given by
F = 6 π ahv ,
(1)
where a = radius of the (spherical) droplet and h = the viscosity of air. Applying this law to the
cases (a), (b) and (c) respectively we have:
mg = 6 π ahv g ,
(2)
E (vE )q - mg = 6 π ahvE ,
(3)
E (V0 )q - mg = 0 .
(4)
The mass of the droplet can be calculated from its size and the density of the oil r (no correction
for the droplet buoyancy in air is made here):
m=
4 3
πa r ,
3
(5)
From these equations we find the charge as follows. First we add equations (2) and (3):
(
)
Eq = 6 π ah v g + v E ,
(6)
which eliminates mg, and gives an expression for q, but which still contains the unknown
quantity, the droplet radius a. To eliminate a, we use equations (5) and (2):
mg =
4 3
π a r g = 6 π ah v g ,
3
(7)
a2 =
9 h
vg .
2 rg
(8)
whence
Substituting from equation (7) into (6) we obtain
9 h 3 / 2 vg
q = 6π
2 ( rg )1/ 2
1/ 2
(v g + v E )
E
,
(9)
which gives q in terms of measured or known quantities. Once the mass of a droplet is known we
can also use the static case with vE(V0) = 0 as a cross check by starting with equation (4) and
solving for the charge q.
Notice that for a given droplet, vg will remain fixed but vE may change if the charge changes.
This means that multiple measurements of a given droplet may show up occasional
inconsistencies that can justifiably be removed from the raw data before further analysis.
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Remember also that the viscosity h is a function of temperature and so care should be taken in
analysing data from different lab sessions.
3.2. Limitations of Stokes’ law. Stokes’ law, equation (1), is derived on the assumption that the
fluid causing viscous drag is a continuous medium. The law cannot be trusted when the droplet
radius a is comparable with the molecular mean free path l, and such conditions may well arise in
the present experiment. It is therefore necessary to keep a watch for systematic errors when the
droplet size is small. Equation (8) shows that vg is a convenient index of droplet size and you
should examine your results for a systematic shift in the values obtained for q with changes in vg.
Notice that the larger droplets (for which Stokes’ law is certainly valid) fall more rapidly than the
smaller ones, and vg is therefore more difficult to measure accurately. A compromise is needed
whereby a droplet size is used that gives tolerable experimental accuracy and yet calls for only
small corrections to the theory.
The value of q found from equation (9) will certainly be the correct value of the charge when
l/a ® 0. We may expect that when l/a is small the departures from equation (9) are expressible
as a power series in l/a, and that only the first term in this series will be important.
If we call qobs the value of q obtained from equation (9) without any correction, then a plot of qobs
against l/a should yield in the first approximation a straight line with its intercept on l/a = 0
giving the first approximation to the true value of charge q. Equation (8) shows that l/a is
proportional to v –1/2, so in practice one may plot qobs against vg –1/2 and fit a straight line to the
data:
qobs = Avg
-1 / 2
+ B,
(10)
where A and B are the line parameters. In the limit l/a ® 0 we find that q = B.
3.3. More accurate corrections to the Millikan experiment. By taking measurements over a
wide range of available variables and droplet sizes a, Millikan showed that Stokes law, equation
(1), should be replaced by
F=
6 π ahv
,
1+ bl a
(11)
where b is a constant. Combining this equation with equations (2), (3) and (5) gives the true
charge q, whereas use of equation (1) gives qobs as in equation (9). Comparing the two, we find
that
3/ 2
1
æ
ö
(12)
q=ç
÷ qobs
è 1 + bl / a ø
or
qobs
2/3
= q 2 / 3 (1 + bl / a ) .
(13)
Given all the above theoretical background, work out the exact procedure for finding q from your
measurements. Decide if the quality of your data justify using this procedure, or a simpler method
described in sections 3.1 or 3.2 is sufficient.
4. The experiment
You will need to work through Exercise before beginning the experiment proper. This will help
you identify the key experimental parameters such as the appropriate droplet size to work with. It
will also highlight some of the experimental problems that may arise with very small or very
large droplets.
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4.1. Start up. Check that the high voltage (HV) unit is plugged into the capacitor assembly and
turn on the direct droplet illumination, HV and timer electronics. Check that the output of the
nebulizer is properly aligned with the input holes in the Perspex shield surrounding the capacitor.
Set the microscope such that the objective lens is about 2 mm away from the window.
Beginning with about 300 V on the capacitor plates, introduce a droplet stream into the apparatus.
Initially you will have to squeeze the nebulizer bulb several times to bring the oil up to the tip of
the nebulizer. Once it is at this level a single sharp squeeze of the bulb should send a plume of
droplets into the apparatus. Looking through the microscope you should see a bright, defocused
mist for a few seconds after squeezing the nebulizer bulb. Now try to adjust the microscope to
bring a few droplets into focus. They should appear as sharp points of light, usually falling or
rising through your field of view. Try varying the HV to check that you can control the speed of
a single droplet and bring it to rest or reverse its motion.
Adjust the level of ambient illumination such that you can see both the microscope graticule and
well focused droplets at the same time. Ensure that droplets fall and rise vertically and that the
graticule is well aligned to the droplet motion in the field. Finally, agree a protocol with your
partner for taking data – you will need to record voltage, fall or rise distance and start/stop times
or interval. You should also note lab temperature as this will change the oil density and air
viscosity.
4.2. Preliminary data acquisition. To do a good job on this experiment your final data set
should contain as many different droplets as possible. At least 100 such measurements are
needed for the analysis to work well. However you need to ensure that you are recording the
useful kind of droplets and so it is absolutely essential that you carry out preliminary data runs
and fully analyse these data sets early on in the experiment.
Acquire a preliminary data set for a moderate number of droplets, say 20–30 to begin with using
as wide a possible range of HV values. For each droplet record sufficient data to enable you to
find its terminal velocity vg under field free conditions, the voltage V0 required to bring it to rest,
and terminal velocities vE under non-zero field conditions. Set up a spreadsheet to allow you to
easily analyse your data and calculate droplet radii, charge etc. Use your preliminary data to
determine the radius in mm and charge on each droplet. Plot a scatter diagram of droplet charge
versus size. Your aim here is to look in the diagram for a charge clustering and periodicity that
could be identified as the elementary charge e. Use your preliminary data run to identify useful
droplet sizes to work with in the light of theory sections 3.2 and 3.3, possible limitations of
Stokes’ law, etc.
4.3 Data acquisition. Based on your preliminary results from 4.2 decide on an optimum range
of voltage, fall time, etc. that minimises systematic errors in your determination of e. Now take a
substantial amount of data for droplets (100 at a minimum) bearing in mind the experimental
subtleties discussed in section 5 below.
5. Additional Experimental Details
5.1. Oil between the capacitor plates. The oil mist enters the capacitor chamber from holes in
the side of the Perspex cover. The insulating properties of the oil are sufficient to change the
electric field in the air gap by as much as 10% or more. It is imperative to keep the chamber free
of surplus oil, and it is worthwhile to remove the top and wipe it out after measuring a few
droplets. Do not use any solvents as these can attack and damage the Perspex cover. Do not
attempt to disassemble the capacitor plates.
5.2. Lighting. You will need to arrange a suitable mix of ambient lighting and direct droplet
illumination to ensure that you can see both the microscope graticule and the droplets easily. If
the background becomes “grey”, such that droplets do not contrast well against it, then cleaning
the apparatus completely helps to reduce the scattered light.
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5.3. Levelling and draughts. A very slight tilt to the apparatus will cause droplets to drift
gradually from the field of view because the electric force E is not precisely vertical. The lateral
motion of the droplets themselves constitutes the most sensitive indicator of tilt. If necessary the
chamber can be adjusted until lateral motion of a selected charge droplet is minimised over
several vertical traversals by placing paper “shims” under the three supporting feet. Note also
that very slight draughts entering the apparatus will blow droplets out of your field of view.
Shield the experiment as necessary to reduce problems from you breath, convection driven by the
lamp, etc.
If droplets drift slowly towards the nebuliser you can gently push them away by a very gentle
puff of air from the nebuliser. Moving the droplet in the opposite direction is also possible but
more difficult: you have to put the palm of your left hand opposite to the nebuliser and blow air
gently from your mouth against the palm so the air is redirected to the apparatus.
5.4. Timing. An electronic timer unit is provided and timing is best done when one student
observes the droplet and operates the timer while the other student notes down the readings and
operates the switching on and off of the voltage supply. To facilitate finding the “start” and
“stop” buttons in the dark it is recommended you stick on them small pieces of a few layers of
sticky tape. Remember to take account of human reaction time by arranging for timer on and off
delays to nominally cancel out.
5.5. Selection of droplets. A single strong squeeze of the nebuliser provides abundant droplets
provided that oil has been drawn up to the top of the nebulizer. A gentler squeeze produces fewer
but larger droplets. The selection of droplets of optimum size is important. If the mass is too
small, Brownian motion causes a large spread of time of fall. On the other hand, too heavy a
droplet, falling rapidly, cannot be timed accurately, and further, it cannot be pulled back up by
available fields when lightly charged. You will need to decide from experiment the optimum
time of fall for best results, and try to select droplets near this size range.
If there are too many droplets in the field of view then keeping track of any one of them is
difficult and tiring. To reject uninteresting droplets you can apply a voltage approximately equal
to V0 and simply wait a few minutes – you will be left with only a few droplets whose charge
approximately balances their weight.
6. Data Analysis
Always plot a preliminary sketch of you data early on in the experiment in order to check general
consistency and to give warning of possible bad techniques before taking a large data set. Extract
the value of the elementary charge from the scatter diagram of droplet charge vs. size. Plotting
charge histograms may be useful here. You can achieve quite high accuracy in the end result but
you will need to account for the spread in the results in terms of the estimated random errors in
measurement. Be alert for systematic errors, which could bias your result, e.g. poor choices of
droplet size or non-vertical fall of droplets. Carefully justify any statistical techniques which you
might use and comment on the applicability of Millikans’ correction.
Note that not all oil droplets will carry single elementary charges, some will carry multiple
charges. You should plot a histogram of the charges carried by the oil droplets with charge on
the horizontal axis and frequency on the vertical axis. Do you notice the data clustering in
groups? What does this tell us?
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7. Technical data
7.1. Plate capacitor
Diameter
Distance between plates
Deviation from parallel
8.0 cm
6 ± 0.05 mm
< 0.1 mm
7.2. Microscope system
Objective magnification
2 ± 0.05×
Micrometer scale range
10 mm
Fine scale graduation
0.1 mm
From the above data, the true scale range is 10 mm / 2 = 5 mm. You may wish to cross check the
optical system using an object of known size such as a fine wire or a “resolution grid”.
7.3. Oil
Density at 15 oC
Density at 25 oC
877 kg m–3
871 kg m–3
7.4. Viscosity of air
h = 1.832×10–5 Pa s
dh / dT = 5×10–8 Pa s K–1
at 293 K
at 293 K
7.5. Earth’s gravity
g = 9.807 m s–2
8. Report
In the report describe what you have learned and achieved. New insights are particularly
valuable. Adhere to the format described in the separate document you were given at the
beginning of the course. Unless told otherwise, write equal amount about this and the other
experiment.
Exercise
You should complete the following brief exercise before starting the experiment. It will help to
highlight some of the experimental issues you may face in the lab.
(a) An oil droplet of 20 mm radius is held stationary when a voltage of 200 V is applied to the
capacitor. If the lab temperature is 20 oC, what is the charge on the droplet? Is this a
reasonable droplet size for use in the experiment?
(b) What is the terminal velocity of a 1 mm radius droplet at 20 oC under zero field conditions?
How long would it take to fall the true scale range of the microscope graticule (= 5mm)? Is
this a reasonable time to take for a single measurement?
(c) An oil droplet at 20 oC takes 2.0 seconds to fall 1 mm under field free conditions. What is its
radius?
Revised:
April 2007 by Roland Smith;
every September from 2008 onwards by Leszek Frasiński
11
Imperial College London
Second Year Physics Laboratory
12
28 September 2015
Imperial College London
Second Year Physics Laboratory
28 September 2015
STUDENT: Please complete boxes marked with asterisk*, then affix firmly
after your Report in lab notebook prior to handing in for Assessment
*NAME
*GROUP
Charges and Fields
EXPERIMENT
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NOT LATE
ASSESSOR
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MARK
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Leszek Frasiński
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REPORT
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