Part of (discluding Data sheets) of First of 12 labs done for Adv. Lab.

1. Classen e/m Experiment Report
Jennifer S. Nalley
Lab Partner: Chris G. Cumby
February 6, 2007
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2. Abstract
The Classen e/m Experiment performed was intended to demonstrate
how the charge to mass ratio of an electron can be determined by
allowing a current run through an apparatus known as the Helmholtz
Coil. It is known that a current running through a solenoid creates a
magnetic field. The Helmholtz Coil setup is roughly based on this
principle. Although the propagated error calculated from our data
differed from the standard deviation by a factor of 10, the results
obtained were considerably reasonable given the large magnitudes
(small numbers) that were recorded.
Introduction and Theory
The experiment, takes advantage of the fact that the electron displays a
unique behavior when introduced into a magnetic field. The primary
apparatus used in this experiment, the Helmholtz Coil, provides a duo of
coils that are wire-wrapped. A Helmholtz Coil, provided with a current
source, in turn yield a magnetic field, which exists horizontally through
the coils. Equipped with the Helmholtz setup, and provided with specific
mathematical formulas:
• Magnetic field B produced at the center of the Helmholtz Coil
8µ o NI B=magnetic field
B= N= turns of coil
125 R R=radius of coil
I= current in coils
µo= permeability of free
space= 4лE(-7) weber/amp- m
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3. *1 weber/meter^2= 1 Tesla
• Formula derived to give the relationship between the charge
and mass of an electron
V= electric potential in Volts
B= the magnetic field from
experiment given formula
e 2V
= r= radius of anode circle around
( Bexp r ) 2 the electron beam
m e/m =electron charge over
electron mass in kg
We were able to measure and manipulate the fundamental
components which are needed to measure the charge to mass ratio
of an electron, and compare it to the accepted value, that is =
coloumbs
1.7588 × 1011
kg
Apparatus and Procedure
The primary piece of equipment used in this lab was a Helmholtz Coil
with a vacuum tube at center. The ideal Helmholtz coil set-up is often
known for, if not partially defined by its geometric proportions. It is the
Helmholtz’s dimensions that allow for the specific equation used for
magnetic field to work without a complex manipulation of any
proportionality constant. The unit has two identical coaxial circular
“coils”. The distances between the two coils are (ideally) proportional to
the radius of either coil. Each coil is wrapped with N turns of wire.
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4. B
In our experiment, the number of wire turns N = 133. We measured
both the distance between the coils, and the radius of the coils in two
ways: from the outer to outer most components, and inner to inner. It
was decided to use an average of these measurements, as they were
the most consistent with the ideal Helmholtz coil proportions. This
choice was determined by our possibly poor assumption that the
manufacturer would have the ideal proportions in mind when it was
designing the apparatus.
The setup we used included:
• CENCO apparatus- a three element electron tube with
adjustable current and plate voltage.
Cathode- serving as an electron source (electron gun).
i.
(-)
Grid- charged to a positive potential to accept and
ii.
focus the electrons from the cathode into a beam. (+)
Anode disk - charged to a higher positive potential to
iii.
actively attract electrons.
• Helmholtz coil(s)
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5. At the midpoint between the coils of the unit (1/2 the radius) was the
anode disk. Mounted upon the disk, rested a vacuum tube with a
filament. In order for there to be visible “action” in a vacuum tube,
electrons must have something to interact with. The vacuum tube
contained enough inert gas, so that the electron beam that was to be
produced would illuminate. From below the tube, the electron exit was
secured in such a fashion that electron rays emitted would eject
vertically, perpendicular to the magnetic field, which would be initiated
via power supply to the cathode. The anode at the center of the setup
was designed to be disk shaped so to surround the point of electron
emission. Like a dart board, the disk was scored with four concentric
circles whose individual radius would become our electron beam target.
In our case, the electron beam darts would come out of the bull’s-eye,
and be made to bend into a semicircle via magnetic field then hit the
disk from which it originated.
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6. The radii of the circular targets were given as follows: 2.0 cm, 1.5cm,
1.0 cm, and 0.5 cm.
Because the earth has its own magnetic field, it was taken into account
both numerically and directionally. We used a compass to position the
apparatus so that the magnetic field running horizontally through the
two coils would be aligned with the direction of the earth’s magnetic
field. The right hand rule proved helpful in the determination of the
Helmholtz field direction. The northern component of the earth’s
magnetic field at our geographical location was found to = 24,708.3
nano-Tesla. *(NOAA)
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7. With the lights off, the current and voltage were adjusted in a variety of
ways to vary the magnetic field, which in turn would control the
curvature of the illuminated electron beam. In order to preserve the
filament, precaution was taken to never exceed a current of 0.7 Amps.
The goal was to aim the beam at each of the given radii one at a time.
The levels for voltage and current were recorded at each radius
respectively for the grid, filament, plate, and field. By changing the
direction of the current, we were able to replicate the process for
readings with our magnetic field going against that of the earth’s field.
Each variation was repeated several times, and is recorded in the data.
With the data gathered and equations provided, we attempted to
calculate the charge to mass ratio of an electron, and compare it to the
current accepted number.
Data and Analysis
The accepted value for an electrons charge/mass ratio is =
coloumbs
1.7588 × 1011
kg
Our average e/m ratio(s) for readings taken:
Lined with earths magnetic field = 2.24065 × 1011 c/kg (± 0.4 × 1011 ) c/
i.
kg
Lined against the earths magnetic field = 2.01474 × 1011 c/kg (±
ii.
0.4 × 1011 ) c/kg
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8. Although our propagated error and standard deviation were off by a
factor of ten, when comparing our average readings to that of the
accepted value, they are not so far off as so to consider the experiment
a total failure.
*The bulk of hard data will be found on the following page(s).
There are several factors that may have contributed to the error in our
obtained calculations. Some of these include:
o On our first day of collecting data, there was no compass
provided. We made due with the assumption, or rather
hope, that the device was already positioned somewhat
correctly. On the second day, a compass was provided, but
we failed to use it to its full potential. We merely noted the
general north direction instead of actually bringing the
compass close to the apparatus and finely positioning it. In
our situation this may have actually led us to more error,
because at a later time I noticed something odd. There were
two identical compasses in the lab, each reading a
completely different, inaccurate north. It is believed that
these two compasses had been previously used near an
electronics lab, which left their orientation way off.
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9. o Out of the four different disk radii, we were consistently
only to line our beam on the outer three. To position the
beam on the innermost circle would have required us to
increase our magnetic field. Our own uncertainty about the
nature of the equipment led us to believe that we needed to
increase our voltage to level that was higher than the 0.7
ampere maximum that the filament preservation warranted
in order to do so.
o We very well could have underestimated the uncertainty of
any of the variables involved: the electron beam radius, the
measured dimensions of the apparatus, the plate, grid, and
field readings. In all of these, we may have been
overconfident in our measurement precision, although
again, as mentioned before, our results were quite good
given the magnitude scale of our data.
o It may have been a mistake to assume the manufacturers
given data to be correct. More measurements could have
been at a minimum verified.
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10. Conclusion
If executed properly with great precision, this experimental procedure
could be used to calculate the e/m ratio with a great accuracy.
Acknowledgements
Resource for earths magnetic field- Geomagnetic Online Calculator
National Geophysical Data Center (NGDC)
NOAA Satellite and Information Series
NOAA website: http:www.ngdc.noaa.gov/seg/geomag/jsp
Halliday/Resnick/Walker- Fundamentals of Physics, 7th edition
Chapter 29, problem # 50
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