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Determining the Charge to Mass Ratio of an Electron via Magnetic Field Deflection
Created by Brian Hallee
Partnered with Joseph Oxenham
Performed October 8, 2010
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Historical Background
A little over a century ago, the structure and underlying mechanisms driving the
atom were still significant mysteries plaguing the professional physicists of the time.
The concept of the atom is documented to have begun around 600 B.C. via the Greeks.
Leucippus and his pupil Democritus assumed that atoms were indivisible solids that
formed the fundamental building blocks of life.1 However, this idea failed to take into
account some of the strange phenomena observed in ordinary matter such as the
“charging” of amber after rubbing it with a piece of fur. Through this, we have observed
a series of desperate bids to conceptualize this phenomenon over the preceding
millennium by a handful of prominent scientists including Benjamin Franklin and J.J.
Thomson. These physicists, chemists, and engineers were inching ever closer to the
theory of electromagnetism and the discovery of subatomic particles. Interestingly, the
original discoverer of the phenomenon we are about to elaborate on, (the electron’s
specific charge), is actually the discoverer of the electron itself. Physicists originally
determined the electron, or “cathode ray” as it was then dubbed, had mass by placing a
paddle wheel in line with the ray; a device developed in 1860’s by Sir William Crookes.2
When a large voltage was applied between a cathode and an anode cathode rays would
travel between the two and turn a wheel demonstrating the fact that the rays had
momentum. In 1897, J.J. Thompson and co. experimented with the properties of
cathode rays known to be electrically charged. He aimed the rays in a predetermined
direction, and subjected them to a magnetic field. Astonishingly, the deflection of these
rays by electric and magnetic fields not only proposed that the rays actually wielded
Page | 2
mass, but that the mass per “corpuscle” was at least a thousand times lighter than the
lightest known element: hydrogen.3 Thomson also realized that the deflection of these
corpuscles deflected in the same manner as electric current, suggesting that the
particles came standard with an electric charge. While the name “corpuscle” was tossed
out by the scientific community in favor of the word electron, J.J.’s influence on the
subject paved the way for more precise measurements and the eventual application of
the electron. One of Thompson’s most ingenious experiments involved going to great
lengths to extract all the gases out of the cathode ray to in order to determine the
charge to mass ratio of the electron. A significant issue troubling physicists at the time
was the unresponsiveness of the rays to electric field. Thompson proposed that the
gases present in the tube were forming a conductor around the ray, (analogous to a
tube of copper), and was preventing the ray from experiencing any force from the
electric field. Once he achieved near-vacuum conditions, the rays behaved as predicted,
and he was able to determine the ratio using derived equations for magnetic fields and
centripetal acceleration.4 (We will view these derivations in-depth in the following
theory section.) Robert Milikan and Harvey Fletcher utilized Thompson’s findings in
1909 to associate the electrons properties with hard, numeric data. Succinctly, their
experiment utilized charged oil droplets, a calculated electric field, and terminal velocity
to come up with the charge q on the droplets. Using Thompson’s specific charge, the
charge of a single electron was found within 1% of the experimentally accepted value
today.5 These early experiments that shed invaluable light on the electron led scientists
of the twentieth century to develop marvels such as the cathode-tube television,
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Figure 1: http://galileo.phys.virginia.edu/classes/636.stt.summer06/pdf%20files/10%20-%20Electron%20Charge-To-Mass%20Ratio.v1.4-10-06.pdf
electronics, and computing technologies. The electron has arguably become the crutch
in our information technology explosion of the 21st century.
Theoretical Basis
This experiment is set up to act upon and observe individual electrons. But just
how do we obtain a steady stream of some of the smallest particles known to mankind?
The theory behind our apparatus used to complete this lab is not so different from the
one concerning Thompson’s some one hundred years ago. The schematic of our
apparatus can be viewed
in figure 1 on the next
page. Succinctly, a strong
potential difference is
used with a specialized
head on the circuit that
actually permits the
electrons to be “shaken”
off of the circuit. In this
lab, that head is made of
Thorium, and the potential difference lies in the 1,500-2,500V range. The electrons
emanating from the Thorium head will want to scatter due to their repulsion and the
uncertain nature concerning where they will actually leave the head. Thus, we utilize an
aperture connected to the negative end of the circuit to draw in the electrons and emit
Page | 4
them in an ordered ribbon. We begin our derivation by applying a few fundamental
concepts of electrodynamics to the equipment just mentioned. Once free of the
conductor, the electrons are accelerated via a potential difference, and thrust into a
magnetic field that will arc the electrons into a near-perfect circular orbit. Thus, we
begin by applying the conservation of energy to the electron while it is being
accelerated by the potential.
∆U=∆ KE (eqn. 1)
Equation 1 states that while the electron is undergoing acceleration due to a potential
difference, its change in potential energy is equal to is gain in kinetic energy. From
introductory electrodynamics6, we know that potential energy is equal to k ¿q q0∨¿r¿.
K = Electricity constant = 1
4 π ϵ 0=8.99 x109 N∗m2
C2
r = Center-to-center distance separating two chargesq = Test chargeq0 = Original charge
Considering both q and r are unknown and vary over time, we use the known potential
difference and value for e as follows:
V=kqo
r=qU∧q=e→U=eV (eqn. 2)
Kinetic energy is represented by the familiar equation12mv2. Thus, we can now fill in
equation 1 with meaningful variables:
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e ∆V=12m∆ v2 (eqn. 3)
We can re-arrange equation 3 to isolate e/m. However, the change in velocity of the
electron is highly unknown, and will have to be substituted using more measurable
properties of this experiment. As demonstrated in figure 1, the electron experiences a
magnetic field the moment it exits the aperture. We mentioned previously that this
field will cause a near circular deflection of the electron. Thus, we can utilize centripetal
mechanics to derive a value for velocity. We begin by noting that the force a charge
experiences inside a magnetic field is equal to the following:
F⃗B=q∗v⃗ x B⃗ (eqn. 4)
You may gather from figure 1 that both B⃗ and v⃗ are in the same plane. Thus, by the
governing of equation 4, the force is orthogonal to the velocity and magnetic field
vectors. Due to the negative charge of the electron, this will cause the path to extend
upwards from the apparatus in figure 1. Equation 4 is useful for modeling directional
properties of the experiment, but, for reasons that will become apparent, we are
currently only interested in the quantitative properties. Therefore, we take the absolute
value of equation 4 as follows:
|q∗v⃗ x B⃗|=evB=FB
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Assuming a radius of 5, the position of the beam
If we apply figure 2 to our set-up, the origin becomes the very exit of the aperature, and
we can safely assume that the force of the magnetic field deflection is equal to the
Newtonian representation of centripetal force.
F centripetal=FB=mv2
r=evB
(eqn. 5)
M = mass of the electrone = charge of the electronB = Abs. value of magnetic field strengthv = Instantaneous velocity of electron in B⃗ fieldr = Radius of circular deflection
In order to model our apparatus after figure two, we need to find a formula for the
radius. This short derivation begins with the formula of a circle centered at the origin:
r2=x2+ y2
Then we need to lift the y-coordinate up so the circle sits on the x-axis:
r2=x2+¿ ¿ x2+ y2+2 yr+r2
The r term cancels out:
0=x2+ y2+2 yr→x2+ y2=−2 yr
We want a positive value for r because a negative radius doesn’t make sense:
¿ x2+ y2∨¿∨−2 yr∨¿ →x2+ y2=2 yr
Thus, radius of the circle in figure 2 can be represented by the following equation:
Page | 7
r= x2+ y2
2 y (eqn. 6)
Equation 5 allows us to isolate v and obtain an equation representing its value as such:
v= eBrm
(eqn. 7)
However, it’s obvious a significant unknown plagues the preceding equations. We have
yet to shed any light as to where the magnetic field is generated, what equipment we
are using to accomplish it, and subsequently what its strength in Teslas might be. The
device utilized in this experiment is called a Helmholtz coil, (developed by Hermann von
Helmholtz in the 19th century), and it produces a practically uniform magnetic field.7
Helmholtz was also keen to derive an equation to govern his coil, and we will re-derive
this quickly treating the formula for the on-axis field due to a single wire loop as an
axiom6 However, it is relatively easy to resolve it starting with the law of Biot and Savart:
B⃗=μ0∋R2
2[R2+x2]32 (eqn. 8)
Where:
μ0 = Permeability of free space = 4 π∗10−7Wb∗mA
I = Current
R = Coil radius, in meters
x = Coil distance, on axis, to point, in meter
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In our case, the Helmholtz coil contains 320 loops tightly wound together. Thus, we
need to take into account more than one loop generating a field. The total current is
equal to nI. Thus, we add this to equation 8 as follows:
B⃗=μ0∋R2
2[R2+x2]32 (eqn. 9)
X is equal to R2
halfway between two coils. Therefore, we can get rid of this variable:
B⃗=μ0∋R2
2[R2+( R2 )2
]32
(eqn. 10)
In a Helmholtz coil, there are actually two coils generating the field; not just one.
Therefore, we can multiply equation 10 by two, and simplify the remaining variables:
B⃗=2μ0∋R2
2[R2+( R2 )2]32
→μ0∋R2
[R2(1+ 14 )]32
→μ0∋R2
R3[54 ]32
→( 45 )32∗μ0∋
¿R
¿
B⃗=8 μ0∋¿
532 R
¿ (eqn. 11)
We are now in position to plug equations 10 and 6 into 7, and substitute 7 into 3 (the
kinetic energy equation) to achieve the following:
eV=12m( eBr
m)2
→V= e B2 r2
2m→
em
= 2V(Br)2
(eqn. 12)
Page | 9
Equation 12 is the governing equation we will utilize to come up with our own
experimental values for e/m. While it could be expanded to include equations 6 and 10
governing B and r respectively, for simplicities sake we calculate these separately using a
spreadsheet and plug them into this extremely simple equation. We will achieve a value
for e/m by varying the current while r diminishes in equal increments, and average the
values to obtain a true specific charge. We follow the same procedure at different
voltages to ensure that our derivation is correct, and that our equipment and procedure
isn’t flawed.
Apparatus
As seen in figure 1, the apparatus contains a slew of components that work
together to achieve electron deflection. In our lab, we utilized a digital TelAtomic
ammeter and analog TelAtomic voltmeter to ensure a high degree of accuracy. The
voltmeter came equipped with a fine and coarse nob, and the ammeter was able to be
set at a 200mA scale. The rest of the components were assembled as one by a
manufacturer. The thorium head, potential-equipped aperture, and Helmholtz coils
were contained within a glass sphere to guarantee that none of the finer components
could be tainted. Likewise, this also served as a safety net to guard observers from the
large voltages present or any stay electrons and x-rays. Lastly, the sphere avoids the
gaseous conductor creation issue experienced by Thompson and many others. Also
included in the sphere was the x-y coordinate grid positioned so the electrons stream
could be quantitatively analyzed by its position and the radius of its circular arc.
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Unfortunately, this grid had, at some point, become skewed due to accidental bumping
or jarring. Thus, as demonstrated in the following calculations section, we were forced
to make corrections to our grid-determined values. The circuit was completed prior to
our arrival to perform the experiment. The apparatus supported regular instructional
banana plug power cords of which demonstrated positive and negative ends via black
and red colored insulation respectively.
Procedure
The actual procedure was relatively quick and painless. The brunt of the effort
came in developing a spreadsheet to contain all of the variables and calculate them
correctly. Again, this was created prior to the experiment in order for us to observe our
values for e/m in real-time and make and changes or re-do’s necessary. Due to the
circuit having been completed beforehand, the procedure began by turning on the
ammeter and voltmeter. Next, we utilized a 0.2A scale for the ammeter, and began
using 1,500V on the voltmeter. In order to achieve this, the coarse knob is turned to
bring the voltage relatively close to the desired value. Only then is the fine knob useful
in “homing in” on a desired value to any degree of precision. The current was initially set
at 0A, as it should be, in order to depict where the electron stream lies with no magnetic
field. This was a consequence of the skewing of the coordinate grid inside the
apparatus. Originally, the stream was to be brought up to the 2cm mark on the y axis at
Page | 11
the specified x value. However, due to the skewing, this had to be altered to 2cm above
the value when no field is present. Thus, when this was acquired, we were able to begin
turning up the current which, as governed by equation 11, linearly increased the
magnetic field. At this point, it is worthwhile to note that the data acquisition phase of
the lab should be completed in a relatively dark room. The grid, having a backdrop of a
musty white/cream color, made it difficult to distinguish the electron beams location
when there was significant light present in the room. We used handheld flashlights to
read the data on the ammeter during the experiment. The x-axis was in units of
centimeters on the grid. Mentioned earlier, the specified x values were 10, 9, 8, 7, 6 and
5 centimeters. We aligned the stream to be two centimeters above these values when
there was no magnetic field present. This was achieved by varying of the current, and
the value in amps was recorded when the beam was aligned properly. This entire
process was done again after setting the voltage to 2,000V, and again at 2,500V. One
last correction needed before finding e/m was applied to the TelAtomic voltmeter. This
voltmeter was found to read about 7% too low. Therefore, we needed to multiply the
reading by 1.07 to have it correlate with the ammeter. In total, we achieved 18
different values of e/m, and they were averaged together in groups with the other
values obtained at the corresponding voltage.
Sample Calculations
Page | 12
As previously stated, we performed our calculations via Microsoft Excel in
separate cells to avoid intermittent error. Thus, our final formula for e/m took the
following form:
e/m = 2*H10/((F10)^2*(E10)^2) (1)
To ensure the accuracy of our cell references and algorithms we will perform a sample
calculation based on the first data point (10cm mark) taken with the voltage set to
2,000V. Due to the skewing of the grid, we subtract 1.25mm from our x value to obtain
98.75mm, or 0.09875m. We assumed that when no field was present that the beam
was reasonably close enough to the x axis to aim for a y value of exactly 2cm when the
field was present. At this point, we have our values for x and y, and we use equation 6
to calculate the arc radius:
r=0.09875m2+0.02m2
2∗0.02m≈0.254m (2)
Now, in order to solve for the magnetic field we need to assume a current value that
gave us the radius in (2). We will assume the value we acquired during this run was
correct. Its value was 0.1507A. The diameter of our coils is given to us in the handout to
be 13.6cm. We have the data necessary to solve for the magnetic field strength using
equation 11.
B=32∗3.14159∗(320coils )∗(0.1507 A)
532∗0.136m
2
∗10−7≈6.38 x10−4 T∗mA (3)
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The last step before determining the specific charge is to apply the correction constant
to the voltage. We are using 2,000V on the TelAtomic analog scale. Thus, we correct it
as follows:
V '=cV=(1.07 )∗2000V=2,140V (4)
Now we are ready to find the specific charge plugging (2), (3), and (4) into equation 12.
em
= 2∗2140V
(6.38∗10−4 T∗mA
∗0.254m)2≈1.63∗1011 C
kg (5)
This is reasonably close to the CODATA8 value of 1.758820150(44)x1011 Ckg
. Thus, we
can take solace in knowing our formulas are correct, and procedure methodology was
sound. Lastly, we came up with a final value for e/m by averaging the 6 runs per voltage
into a single value, and subsequently averaging the three averages generated. This was
achieved using the AVERAGE function built into excel, and can be viewed first hand on
the accompanying disc.
Voltage-Specific Average: = AVERAGE(I6,I7,I8,I9,I10,I11)
Overall Average: = AVERAGE(E12,E21,E30)
It will also be of importance for us to look at the standard deviation, and error of the
mean of our data. This is a crude representation of how well the data fits together or
how bad it varies. The Excel-calculated value for standard deviation can be found in the
Page | 14
appendix of this report. We will attempt to recreate it below by finding the standard
deviation of the third series of runs at 2,500V:
σ=√∑in
(x i−x)2
n=√(1.632−1.738)2+(1.669−1.738)2+(1.624−1.738)2+(1.723−1.738)2+(1.833−1.738)2+
(1.947−1.738¿¿2)6
∗1011¿
= 1.168x1010
This correlates closely with the appendix value of 1.184x1010. Thus we can be sure the
formulas and cells are referenced correctly. We can take this value a step further and
easily calculate the standard error of the mean shown below:
σ n=σ
√N=1.168∗10
10
√6=4.77 x109
This is not terribly close to the value for all the data located in the appendix. Therefore,
due to its extensive use in the discussion section, we will sample the calculation used to
find the exact error any two values of the same type:
%Error=|σn−actual−σn−calc|
σn−actual
∗100%=|2.79−4.77|
2.79∗100%
≈71%error
We have used the small-N definition of the error of the mean due to the relatively small
amount of data points we have to work with in this experiment. We have a total of 18
values of e/m, which is far too little to take into account crucial effects that develop in
large data sets.
Page | 15
Finally, due to the uncertain nature of this experiment, we are required to find the
relative error of the specific charges gathered. We will first find the relative error of the
first series (V = 1,500V), and it can be found using the following formula:
%Rel .Error= Absolute ErrorMeasurement
At this point, we are required to make some assumptions. For reasons we shall develop
later, we will assume that we have a degree of accuracy of two significant figures. Thus,
relative to our average value acquired for series 1, our absolute error becomes 1x1010 Ckg
. Thus, the percent error is as follows:
%Rel .Error=1 x1010
Ckg
1.64 x 1011Ckg
∗100%≈6.1%
Discussion
As proved in the theory section of this report, the formula governing e/m was
the product of a tiring combination of separately derived formulas. Thus, it seems fitting
that we utilize dimensional analysis to ensure the units come out to be correct. This is
quickly proved below:
Vo lts=WA
= JA∗s
= N∗mA∗s3
= kg∗m2
C∗s2
Page | 16
Teslas=V∗s
m2= N
A∗m= kg
A∗s2= kgC∗s
From eqn. 12:
em
= 2VB2 r2
=( kg∗m2
C∗s2)
( kgC∗s
)2
∗m2
=( kg∗m2
C∗s2 )∗( C2∗s2
kg2∗m2 )=( kg∗C2kg2∗C )= Ckg
Now we can be sure the derivation is correct, and we move on to the experimental
errors. Upon averaging all values obtained for the specific charge ratio, we obtained a
value of 1.70x1011 Ckg
. This is in contrast to the 2006 CODATA accepted value of
1.758820150(44)x1011 Ckg
. Right away, we can calculate the experimental error of our
value by the following calculation:
% error=| em accepted
− em experimental
|em accepted
∗100%=|1.76 x1011 Ckg−1.70 x 1011 C
kg|1.76 x 1011
Ckg
∗100%
≈ 3.41% error
This is a very reasonable error considering the multitude of factors that worked against
us in this experiment. First, we are perhaps allotting more precision to the value we
acquired than even ought to be bestowed. This is due to the somewhat uncertain value
of y stemming from the skewed nature of the grid. When trying to depict where exactly
the position lied 2cm above the “field-less” beam, we can, at most, state a height with a
Page | 17
degree of accuracy to two significant figures. Thus, from the rules of multiplication of
significant figures, the value we acquired should have an error spanning in both
directions of 1x1010 Ckg
. We can quantitatively get a handle on this error by using the
percent relative error formula from our sample calculations as follows:
%Relative Error=Absolute Error
Overall AVG . specific charge=
1x 1010Ckg
1.70 x1011Ckg
∗100%
≈5.9%Relative erro r
Therefore, we have an upper and lower bound for specific charge of 1.8 x1011Ckg
and
1.6 x1011Ckg
respectively from the formula below:
em
=¿
Apart from the uncertain nature of y, other factors that likely played a role in our
error naturally include the skewing of the grid, and the uncertainty of the
voltmeter. First, while the x-coordinate correction is extremely precise, it was not
mentioned as to how this value came about, or how accurate the correction
factor is. Likewise, the beams width proved to be a bit wider than the grid lines.
Thus, the degree of accuracy to which we were able to align the beam on the
grids was in no way acceptable to three significant figures or more. Aside from
this, the lab report developed by the instructor stated the voltmeter read 7% too
Page | 18
low. We assume this requires a correction constant of exactly 1.07, but this is not
likely the case. From equation 12, any error in measuring V is directly passed on
to the specific charge ratio. Thus, from a potential perspective, we have both the
multimeter’s raw uncertainty and the correction constant uncertainty to take
into account. Combining all of these factors, and bearing in mind that both e and
m are infinitesimally small quantities, an error of 5% seems rather reasonable.
There are quite a few trends that can be gathered from the data located in the
appendix of this report. First, and perhaps most importantly, the specific ratio of
e/m tends to increase as the potential is increased. Upon reviewing the
properties of this experiment, it should be evident that at such large potential
differences, relativistic effects come into play. This is demonstrated cleanly by
one of the most generally known equations concerning relativity:
E=mc2 or more generally m≈E
v2
This denotes that as velocities reach a relativistic speed, the mass will begin to
decrease. At the kV level, this is exactly the phenomenon we are observing as
electrons are entering the vacuum in the apparatus at enormous speeds. Thus,
as mass decreases m becomes smaller in the denominator, subsequently
increasing the ratio. This same mathematical effect is what governs the fact that
specific charge increases with decreasing x-values. Referring back to equations 6
Page | 19
and 12, you can see that the radius varies directly with x, and e/m is inversely
proportional to the square of the radius. Therefore, we see r quickly decreasing
in the denominator causing the ratio to increase. Consequently, both of these
trends are bound by mathematical fundamentals, and serve as the reason as to
why so many different runs were completed.
There is one final factor that a reader unversed in physics would likely feel both
ours and Thompson’s experiments left out. This factor is the downward force of
gravity, and holistically it seems as though it should play a significant role in
determining the arc of the beam once it enters the magnetic field. This issue can
be quelled qualitatively by envisioning a thumbtack and your average refrigerator
magnet. As you move the magnet relatively close to the pin, it picks it up with
comparative ease. Although we may take this fact for granted, we do not always
conceptualize that the magnet in our hands has just trumped the entire earth’s
gravitational pull on that tack. Thus, gathered from this analogy, we can be sure
that magnetic and electrostatic forces are many magnitudes greater than
gravitational force. Therefore, it is safe to assume, as Thompson did, that gravity
will play virtually no role in determining the net force on the electrons in our
apparatus.
When Thomson carried out his experiment, he tested his results against several
different mediums and properties such as metals, gases, etc. His value, however,
Page | 20
remained steady throughout which suggested that the ratio was independent of
the gas in the tube and the metals used to construct the cathode.9 If this is true,
then it must follow that his miniature corpuscles must be a constituent element
of every atom.
What may be the most impressive property of Thomson’s experiment is the
degree of accuracy he achieved with his initial run. In his statement to the Nobel
Prize committee and scientists from all over, he mentions a single numerical
value of this work: 1.7x107.10 On the face, this may seem orders of magnitude off
base. However, after a bit of tweaking this value turns out to be very relevant in
terms of SI units. In his day, electrodynamics utilized a system of units known as
the C.G.S. (centimeter-gram-second system). Therefore, Thomson’s value of
specific charge was measured using a subset of this system known as electro-
magnetic units. Specifically, his value was measured in abCoulombs per gramme.
Barring the unnecessary history and theory of this system, we will treat the
following as an axiom:
1C=10−1 AbCoulombs
We wish to garner a measurement in Coulombs per kilograms as follows:
1.7 x107AbCg
∗( 103 gkg )∗( 1C10−1 AbC )=1.7 x 1011 Ckg
Page | 21
Ignoring the errors in both of our experimentations, this is exactly the value we
acquired over our 16 runs. Thus, we can not only take solace in our own value
acquired, but also further appreciate the precision of Thomson’s value realizing
the primitive and foundational nature of his work.
Page | 22
ENDNOTES
Page | 23
APPENDIX – RAW DATA
Run 1: V' = 1,500V
x' (m) y (m) x I (A) r (m) B V' V e/m0.1 0.02 0.09875 0.135 0.253789 0.000571 1500 1605 1.53E+11
0.09 0.02 0.08875 0.1657 0.206914 0.000701 1500 1605 1.53E+110.08 0.02 0.07875 0.2033 0.165039 0.00086 1500 1605 1.59E+110.07 0.02 0.06875 0.2579 0.128164 0.001091 1500 1605 1.64E+110.06 0.02 0.05875 0.3369 0.096289 0.001426 1500 1605 1.7E+110.05 0.02 0.04875 0.4507 0.069414 0.001907 1500 1605 1.83E+11
Average value of e/m: 1.63688E+11
Run 2: V' = 2,000V
x' (m) y (m) x I (A) r (m) B V' V e/m0.1 0.02 0.09875 0.1507 0.253789 0.000638 2000 2140 1.63E+11
0.09 0.02 0.08875 0.1842 0.206914 0.000779 2000 2140 1.65E+110.08 0.02 0.07875 0.2286 0.165039 0.000967 2000 2140 1.68E+110.07 0.02 0.06875 0.2906 0.128164 0.00123 2000 2140 1.72E+110.06 0.02 0.05875 0.3788 0.096289 0.001603 2000 2140 1.8E+110.05 0.02 0.04875 0.512 0.069414 0.002166 2000 2140 1.89E+11
Average value of e/m: 1.72861E+11
Run 3: V' = 2,500V
x' (m) y (m) x I (A) r (m) B V' V e/m0.1 0.02 0.09875 0.1686 0.253789 0.000713 2500 2675 1.63E+11
0.09 0.02 0.08875 0.2045 0.206914 0.000865 2500 2675 1.67E+110.08 0.02 0.07875 0.2599 0.165039 0.0011 2500 2675 1.62E+110.07 0.02 0.06875 0.3249 0.128164 0.001375 2500 2675 1.72E+110.06 0.02 0.05875 0.4193 0.096289 0.001774 2500 2675 1.83E+110.05 0.02 0.04875 0.5643 0.069414 0.002388 2500 2675 1.95E+11
Average value of e/m: 1.73811E+11
Overall Average: 1.7012E+11
Page | 24
Standard Deviation: 1.184E+10Standard Error of Mean: 2.791E+09
Page | 25
APPENDIX – DISC CONTENTS
ROOT DIRECTORY
o ELECTRON CHARGE TO MASS RATIO.DOC
THE OFFICIAL WORD 2003 FORMAT OF THE SPECIFIC CHARGE RATIO LAB REPORT
o FIGURES 1 AND 2
.GIF COPIES OF THE FIGURES DISPLAYED IN THE THEORY SECTION OF THIS LAB REPORT
o LAB SPREADSHEET.XLS
EXCEL 2003 FORMAT OF THE RAW DATA TAKEN DURING THE EXPERIMENT. THIS ALSO
CONTAINS FORMULAS USED TO FIND THE FINAL VALUES LOCATED IN THE RAW-DATA
SECTION OF THE APPENDIX IN THIS REPORT
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1 Berryman, Sylvia, "Democritus", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.),http://plato.stanford.edu/archives/fall2008/entries/democritus
2 Crookes, William (December 1878). "On the illumination of lines of molecular pressure, and the trajectory of molecules". Phil. Trans. 170: 135–164.
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4 American Institute of Physics. (1997, March). A Look Inside the Atom. Retrieved October 17, 2010, from American Institute of Physics: http://www.aip.org/history/electron/jjhome.htm
5 University of Alaska: Fairbanks. (n.d.). The Millikan Oil Drop Experiment. Retrieved October 17, 2010, from University of Alaska: Physics Department: http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/ryan_mcallister/slide3.htm
6 Hugh D. Young, R. A. (2007). University Physics. Pearson Addison-Wesley.
7 Crowell, B. (2009). Electromagnetism. Retrieved October 18, 2010, from Light & Matter: http://www.lightandmatter.com/html_books/0sn/ch11/ch11.htm
8 Peter J. Mohr, B. N. (2007, December 28). CODATA Recommended Values of the Fundamental Physical Constants. Retrieved October 19, 2010, from National Institute of Standards & Technology (NIST): http://physics.nist.gov/cuu/Constants/codata.pdf
9 Franklin, A. (2009). Appendix 7: Evidence for a New Entity: J.J. Thomson and the Electron. Retrieved October 21, 2010, from Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/physics-experiment/app7.html
10 Thomson, J. (1906, December 11). Carriers of negative electricity. Retrieved October 21, 2010, from NobelPrize.org: http://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-lecture.pdf
