Student Name and I.D.: Peter
Lab session: Lab 2B
Submission
Date: 4-4-2001
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1.
Introduction
Figure 1: e/m apparatus
One
of the methods for measuring the electronic charge to mass ratio (e/m) is the
use of the e/m apparatus as shown in Figure 1. A beam of electrons is
accelerated through a known potential, so the velocity of the electron is known.
A pair of Helmholtz coils produces a uniform and measurable magnetic field at
right angles to the electron beam. This magnetic field deflects the electron
beam in a circular path.
The
aim of this experiment is to determine e/m by measuring the accelerating
potential, the current of the Helmholtz coils and the radius of the circular
path of the electron beam.
2.
Theory
For
a charged particle of charge q moving with velocity v in a magnetic field
(B),
Since the electron beam is perpendicular to the magnetic field (in this experiment),
Magnetic force, Fm = evB
------------------------------- [1]
Since the electron moves in circular path,
Centripetal Force, FC = mv2/r
------------------------------- [2]
As Fm = FC, combining equations [1] and [2], we have
e/m= v/(Br)
------------------------------- [3]
Kinetic energy gained by the electrons when accelerating through the accelerating potential = K = ½ mv2. Hence ¡K
The magnetic field produced near the axis of a pair of Helmholtz coils, ¡K
Substituting
equations [4] and [5] into equation [3], we have ¡K
3.
Procedure
Before
the experiment started, the light of the laboratory was turned off and a hood
was placed over the e/m apparatus. The toggle switch was flipped to the e/m
position and the current adjust knob for the Helmholtz coils was turned to OFF
position. The power supplies and meters to the front panel of the e/m apparatus
were then connected as shown in Figure 2.
Figure 2: Experimental Setup for e/m
experiment
The current adjust knob for the
Helmholtz coils was slowly turned clockwise. The cathode was heat up and the
electron beam was then adjusted such that it was parallel to the Helmholtz
coils.
The current to the Helmholtz coils,
the accelerating voltage and the radius of the electron beam were recorded. The
values of the electrode voltage to be performed were 150V, 200V and 250V.
4.
Result and Analysis
a = 0.15m
N = 130 turns
A graph of e/m against the
accelerating potential is plotted.
Figure
3: e/m against the accelerating potential
5.
Error Analysis
£GV = + 0.5V
£GI = + 0.0005A
£Gr = + 0.00001m
6.
Discussion
1)
The order of the experimental values of e/m agrees with that of
the accepted value, but the magnitude of the experimental values of e/m
does not agree within the experimental error with the accepted values.
There are
two main reasons. Firstly, error is introduced when measuring the radius of the
path of the electron beam. Secondly, The electron beam is not adjusted well and
thus it may not be parallel to the Helmholtz coils. (These will be discussed in Error
Source.)
2)
The graph of the theoretical accepted values of e/m against V is a
horizontal line, therefore it does not depend upon V. But the graph of
experimental value against V does not give a horizontal line (slightly inclined)
probably due to the presence of error source.
However,
the size of error bar depends on V: the larger V, the smaller the size of error
bar. Therefore, high setting of V is the best for measuring e/m (but it should
not exceed the limit of 6.3V because this will burn out the filament and destroy
the e/m tube).
7.
Error Source
1) Error in measuring the radius of the circular path: this may be because the electron beam is not bright enough. Also, the radius is determined by halving the measured values of the corresponding diameter. Error in the measured values of diameter is then significant.
2) The electron beam is not parallel to the Helmholtz coils. The velocity vector of the electrons is then not perpendicular to the magnetic field.
3) Parallax errors may have occurred.
4)
The current setting of the Helmholtz coils is not well adjusted. This
makes the electrons do not follow a path that is roughly centered in the tube.
8.
Suggestion and improvement
Some precautions to the experiment are:
1) The voltage for the electron gun heater should not exceed 6.3V.
2) The Helmholtz current should not exceed 2A.
3) The electrode voltage should not exceed 300V.
4)
The experiment wiring should not be altered.
Some improvement to the experiment:
1) Make sure that the current setting of the current setting of the Helmholtz coil is adjusted so that the electrons follow a path that is roughly centred in the tube.
2) Make sure that the radius is measured along the line corresponding to the diameter.
3) Focus the electron beam so that it is sharp enough for measurement.
4)
Avoid parallax error.
9.
Conclusion
The order of the experimental values e/m is consistent to that of the accepted value, which is of 10-11, and the magnitude of the experimental values is close to the accepted one. Also, it is found that a high value of V is the best for measuring e/m.