current passes through both of the coils in the same
direction.
- If the electron beam deflects downward, swap the
connections on the 3.5 A output terminals on the
Power Supply.
- If the electron beam forms a spiral, rotate the tube on
the platform until a closed circle is formed. You may
also need to rotate the platform to the right or left to
align the magnetic field generated by the Helmholtz
coils with Earth’s magnetic field.
7. Disconnect the wire between the Accelerating Voltage
positive terminal and the Deflection Plates Upper terminal.
8. On the Tunable DC (Constant Voltage) Power Supply II,
adjust the voltage output to the Accelerating Voltage to
optimize the focus and brightness of the electron beam.
Record data
1. Read the current display to find the current I
H
through the
Helmholtz coils. Record the value in Table 1.
2. Read the voltmeter and record the Accelerating Voltage U
in Table 1.
3. Measure the radius r of the electron beam’s circular path.
Look through the e/m tube at the mirrored scale. To avoid
parallax errors, move your head to align the electron beam
in the tube with the reflection of the beam as you see it in
the mirrored scale. Measure the radius of the electron
beam path as you see it on both sides of the scale and
average the results. Record the average radius of Table 1.
4. Collect additional trials of data using different accelerating
voltages and current through the Helmholtz coils.
NOTE: If you lose the electron beam while
adjusting the Accelerating Voltage, repeat Steps
5 through 7 of Adjust voltages and current.
Table 1. Data
Trial
U (V)
I
H
(A)
R (mm)
e/m (C/kg)
% error
1
2
3
4
5
Analysis of e/m measurements
The magnetic field B generated in a pair of Helmholtz coils is
proportional to the current I
H
passing through a single coil. The
constant of proportionality k can be determined from the coil
radius R and the number of turns N on the coil with the following
equation:
With this expression for B, the initial formula for e/m,
becomes:
In this experiment, R = 158 mm, N = 130 turns per coil, and
= 4 ×10
-7
.
The accepted value of the charge-to-mass ratio e/m is
1.75×10
11
C/kg.
Demonstrations
Deflect the beam using an electric field
With no current in the Helmholtz coils, deflect the beam using
the deflection plates:
• Connect a wire between the Accelerating Voltage positive
terminal and the Deflection Plates Upper terminal to make
the electron beam deflect upwards.
• Switch the wire to the Deflection Plates Lower terminal to
make the electron beam deflect downwards.
Deflect the beam with a permanent magnet
Hold a permanent bar magnet near the tube to show the effect
of a magnetic field on the electron beam. Switch between
holding the north end and the south end of the magnet near the
beam.
Rotate the tube
Rotate the tube so that it is oriented at an angle with respect to
the magnetic field from the Helmholtz coils. As you rotate the
tube, observe how the beam deflection is affected.
Deflect the beam using Earth’s magnetic field
With no magnet and no curent in the Helmholtz coils, rotate the
tube or the entire apparatus to see the deflection of the beam
due to the Earth’s magnetic field. Is the direction of the
deflection of the beam as you expect?
Electron Charge-to-Mass Ratio | SE-9629
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