1. Purpose Determine the charge to mass ratio (e/m) of an electron.
Design your own experimental procedures. Decide
what measurements to take,
the range of values you will measure,
how to obtain the uncertainties of measured and computed quantities,
how to analyze the data graphically, and
what error propagation procedures to perform.
Gain experience in writing a report in the form of a scientific paper.

2. Background
1892: Hendrik Lorentz introduces the force acting on a charged particle
moving through a magnetic field (the Lorentz force, or magnetic force):
The cross product means:
Only the components of the vectors v and B that are perpendicular to each other contribute to the force.
The force is perpendicular to both the vector v and the vector B.

3. The charge here is assumed to be positive.
(points into the page) q
The charge here is assumed to be positive.
For negative charges the force would be downwards.

4. circular path r q
(points into the page) q
The force continually changes the direction of the velocity, but not it’s magnitude.
The direction of the force changes also and it’s magnitude also remains the same.

5. For Circular Motion (Radius r)
Derive expression for e/m(v,B,r)=…..

6. Getting the electron up to speed …and knowing what that speed is.
Speed increases as electrons approach plate
Some electrons miss the plate and fly
through the hole in the plate.
 electron beam comes out of hole.
filament
electrons v v v E
Ifilament
Many electrons return
because they hit the plate.
(Note: return path of electrons
is opposite to conventional
current.)
filament
Voltage
(6V)
accelerating
voltage
(150V-300V)
The filament current heats up the filament  electrons get enough energy to exit the filament.
Electrons get accelerated by the force in the electric field (created by the accelerating voltage).

7. Getting the electron up to speed …and knowing what that speed is.
electron has potential energy = eVacc
and kinetic energy = 0
electron has potential energy = 0
and kinetic energy = ½ mv2 v v v
Conservation of energy:

8. Generating the Magnetic Field
A pair of Helmholtz coils a B I I I
Magnetic field in the
center of the Helmholtz
coil pair. I
N turns of wire
in each coil.

9. Power Supplies Before you switch on the power supply:
Identify all components according and verify that all connections are as
shown in the lab manual.
Identify on the high voltage power supply the dial that controls the
accelerating voltage: Turn that dial all the way counterclockwise into the
zero position.
Identify on the low voltage power supply the two dials that control the
current through the Helmholtz coil: Turn both dials (voltage control and
current control) counterclockwise into the zero position.
Identify on the low voltage power supply the heater voltage dial. This is a
step dial. Verify that it is set to 6 Volts.

10. High Voltage Supplies
Older model
Newer model

11. Low Voltage Power Supplies
Older model
Heater voltage:
must be dialed
to 6V
Newer model
Helmholtz coil
current and
voltage
regulation

12. Switching on the Power Supplies
Now switch on both power supplies. Check and make sure that the Helmholtz coil current is zero and the accelerating voltage is also zero.
Look at the tube: You should see the filament glow orange/yellow.
Carefully dial up the accelerating voltage on the high voltage power supply to about 200V (never exceed 300V).
Regulating the current in the Helmholtz coil:
There are 3 knobs that control voltage and current through the Helmholtz coil:
Current adjustment knob for Helmholtz coils on the e/m apparatus.
Current adjustment knob on low voltage power supply.
Voltage adjustment knob on low voltage power supply.
 Next page: how to use these three knobs.

13. Regulating the Current in the Helmholtz Coil:
First turn DC VOLTAGE ADJUST to zero (all the
way counterclockwise)
Then turn DC CURRENT
ADJUST all the way
clockwise (max. current).
Then turn current adjust knob
On the e/m apparatus
all the way clockwise
(max. current).
The current meter should STILL READ ZERO.

14. Regulating the Current in the Helmholtz Coil:
Carefully turn DC VOLTAGE
ADJUST clockwise.
Watch the current meter!
When current meter reaches
2 Amps: Stop!!
Leave at this setting!!
From now on only regulate
the current with this knob on
the e/m apparatus
Totally clockwise = 2A
Totally counterclockwise = 0A

15. Switching Off Power Supplies
Before you switch off the power supply:
Identify on the high voltage power supply the dial that controls the
accelerating voltage: Turn that dial all the way counterclockwise into the zero position.
Identify on the low voltage power supply the two dials that control the current through the Helmholtz coil: Turn both dials (voltage control and current control) counterclockwise into the zero position.
Now switch off.

16. Hints
When measuring the radius of the electron’s circular path, take advantage of the mirror-scale behind the tube:
- Move your head to the left or right until the mirror image of the beam overlaps the actual electron beam. Then read off the scale.
- Repeat the procedure for the left side.
- Determine diameter from the two values (radius is half of that).
Read off right side
Read off left side

17. Important for the Longevity of Apparatus
Never exceed 300V on the accelerating voltage. Always monitor this voltage on the attached volt meter when changing that voltage.
Never exceed 2A on the Helmholtz coil current. Always monitor this current with the attached current meter when changing that current.
Always dial down accelerating voltage and Helmholtz current to zero before switching off the power supplies.

18. Lab Report
Lab report must be written in the form of a scientific paper
(see example in the back of the lab manual).
Each person must write their own lab report
(no group report for this experiment).
You have 1 week to complete and submit the lab report.
Late lab reports will get a deduction of 5% per day late
(e.g., if your report is 3 days late you will only get credit for 85% of the score that you would have gotten if you submitted on time).