Goals: To study the motion of an electron beam in electric and magnetic fields, and to measure the charge-to-mass ratio of electrons.
Pre-Lab: Problem sheet on the e/m apparatus
CAUTIONS:
1. This experiment uses high voltage and high current power supplies. Be careful around these! Do not plug in or unplug any wires or touch any wires unless you are sure that the electric power to the wires is turned off.
2. Do not operate the high voltage power supply above 4.5 kV, as this will burn out the filament that supplies the electron beam.
3. Do not operate the high current power supply above 10 Amps, as this will blow the fuse in the ammeter.

Method:
A. Magnetic Field Only
1. Make sure that both electric field plates are grounded (i.e. are connected to the negative terminal of the high voltage power supply).
2. Turn on the high voltage power supply, and increase the voltage until you can see the blue light from the path of the electron beam. Why does the light get brighter as you increase the voltage?
3. Turn on the high current power supply, and observe what happens to the electron beam. From your observation, what can you conclude about the direction of current flow in the Helmholtz coils?
4. In the pre-lab, you should have derived a formula for the charge-to-mass ratio of a charged particle travelling in a constant magnetic field. Your expression should involve the variables V (the voltage difference between the cathode and anode in the accelerating tube), R (the radius of the particle's circular path) and B, the strength of the magnetic field.
We will determine the magnetic field strength in the region between the Helmholtz coils using the following formula:

In this expression, I is the current that passes through the coils, R is the radius of the Helmholtz coils (also equal to the distance between the two coils), and N is the number of turns on each coil.
You'll need to devise a method for measuring R. Describe your method.
5. Make a table of all the quantities you need to measure in order to determine the electron's charge-to-mass ratio. Then make your measurements.
6. Use your measurements to determine q/m, the charge-to-mass ratio of the electron. Compare your results with the ratio determined from the values of q and m given in the textbook.
7. What effect does Earth's magnetic field have on this experiment ? Do you think it is an important effect ? (Consider what you found out in Lab D8). How could the experiment be designed to minimize the effect of Earth's magnetic field ?
B. Electric field only
1. Turn off both power supplies.
2. Locate the wire that connects the bottom electric field plate to the high voltage power supply. Leave the connection to the electric field plate intact, but move the connection at the other end of the wire from the negative terminal of the power supply to the positive terminal.
3. Now turn on the high voltage power supply. What direction is the electric field? What is the shape of the path of the electron beam? Find a mathematical equation for the shape of the path, i.e. y-coordinate as a function of x-coordinate. (Hint: You've seen this kind of motion in problems we did last semester.)
4. Now try varying the voltage. Why doesn't the path of the electron beam change ? Explain using the formula you found in question 3. (Hint: look at the wires coming from the high voltage power supply. Note that the voltage that accelerates the electron beam from the cathode to the anode is the SAME as the voltage applied to the electric field plates.)
5. As accurately as you can, measure at least three sets of x- and y-coordinates for the electron beam's path. Where should you choose the origin of your coordinate system?
6. Make a graph of y vs. x² from your measurements of the coordinates. What shape do you expect this graph to have? The slope of your graph corresponds to a particular aspect of your experiment. What quantity is represented by your slope? Compare the slope of your graph with the measured value of that quantity.
C. Electric and magnetic fields
1. With the high current power supply still turned off, set the high voltage power supply to 3 kV.
2. What is the direction of the electric force on the electrons? If you want to balance that force with a magnetic force, what must be the direction of the magnetic field you should apply? Is this the same direction as the magnetic field you used in part A? If not, what must you do in order to achieve a magnetic field in the desired direction? Don't turn on the high current power supply yet!
3. Once you have made any adjustments necessary to make a magnetic field in the desired direction, PREDICT how much current you will need to supply to the Helmholtz coils in order to make the electron beam follow a straight path. You will need to use the formulas from parts A and B.
4. NOW turn on the high current power supply and test your prediction. Were you correct?
5. Turn off the high current power supply, and turn the high voltage power supply up to 4 kV. What must you do to the current if you are to again balance the electric force by a magnetic force? Test your prediction by turning on the high current power supply.