Physics PHYS 353 Electricity and Magnetism I Lab Experiment #2

Deflection of Charged Particles by an Electric Field I. Introduction In this lab we will use a cathode ray tube to produce and accelerate a beam of electrons. We will then measure the deflection of these electrons in a static, uniform electric field. The results of a theoretical prediction based on Coulomb's and Newton's Laws will be compared to our experimental results. II. Theory Figure 1 below presents a schematic diagram of the deflection plates in our experimental setup, which we will use in making our calculations. The electron is incident on a region of uniform electric field in the y-direction. This electric field exerts a force on the electron while it is in this region. Therefore, when it leaves the electric field region it will have a component of velocity in the y-direction, which will cause it to hit the screen off-center.

Figure 1. Schematic diagram of deflection plates in our experimental setup. As we showed in class, the relationship between the deflection D, and the deflecting voltage VD for an electron that has been accelerated through a voltage V is

dVVLD D

2l

= .

In this lab you will be testing this prediction by measuring D as a function of VD for several values of V. III. Experimental Apparatus The apparatus for this experiment consists of a cathode tray tube RCA 3RP1, and the resistor chain voltage divider and HV power supply necessary to operate it. Construct the circuit as

described in Exercise #2 and test it out. Use a ring stand and clamp to support the CRT. Attach 0-30V power supplies to the deflection plates as shown in the schematic in Appendix A. IV. Experimental Procedure The basic procedure for this lab is as follows:

1. Find the electron beam. Turn on the HV supply and adjust the accelerating voltage to about 300V. Adjust the focus and intensity controls to obtain a clear, sharp beam spot on the screen.

2. Deflect electron beam. Now turn off the supplies and connect the beam

deflection voltage to the "vertical plates". These are the ones closest to the base, and connected to pins 6 and 7.

3. Set up to reduce the effect of the Earth's magnetic field. As you know a

moving charge (the electron beam) can be deflected by a magnetic field. What is the force on a moving charge in a magnetic field? Can the force be zero? Arrange the CRT tube so that the Earth's magnetic field will not deflect the electron beam. What is the direction of the Earth's magnetic field at the CRT? When you have the tube orientated correctly the deflection should not change when the accelerating voltage changes. Can you explain why?

4. Measure electron beam deflection. Now let's measure the deflection of the

electron beam. Keeping the accelerating and focusing voltages constant, measure the deflection D as a function of deflecting voltage VD for your value of V.

5. Change Beam Voltage. Now change the beam voltage, V, three more times to

350 V, 400 V, 450 V, and 500 V. You may need to readjust the intensity and focus. Again measure the deflection, D, as a function of deflecting voltage, VD.

V. Results Make a plot of D versus VD for each of your values of V. Be sure to include error bars for each measurement. Put the theory curve on each plot. Does the theory prediction agree with your measurement? In order to determine the theory curve, you will need to know L, the distance from the deflection plates to the screen, l , the length of the deflection plate, and d, the separation of the deflection plates. Rather than trying to measure them directly, you can measure these quantities from the photographs of the electron gun in Appendix B. First determine the scale from the ruler in the photograph, then determine l and d. The distance L can be measured but using the photograph to find the distance from the end of the deflection plate to the edge of the base, then measuring from the edge of the base to the screen on the outside of your intact CRT.

Here are some things to think about. I am sure you can add more.

1. From what point between the plates should we measure L? In class we decided, (somewhat arbitrarily) to measure from the center. How big of an effect might this have?

2. Why are the deflection plates flared instead of completely flat? 3. What is d if the plates are flared? Can you calculate an "effective d" that would be

appropriate? 4. You know the field between the plates is not perfectly uniform, especially because

of the fringe filed near the edges. What effect will the fringe field have? Could it be reduced?

5. Is the force of gravity on the electron of any importance? 6. In the discussion of the electron beam motion we have not considered interactions

between electrons in the beam. How can this omission be justified? 7. How well do you know the voltages? How well do you trust your measured

dimensions? VI. Laboratory Report

1. In your laboratory report be sure to include a detailed description of how you made your theoretical calculation, as well as describe the apparatus and the procedure you used to make the measurement.

2. You definitely should include a schematic diagram of the experiment as it actually was (i.e. don't count on it being exactly what is in this lab handout.)

3. You should have plots of D versus VD for each of your values of V, with uncertainties.

4. You should include some discussion of each of the questions above. 5. You should have a description of how you obtained these uncertainties. In the

conclusion you should tell us the "bottom line" -- is this theoretical model of the electron deflection consistent or not with the measurement.

Appendix A -- Cathode Ray Tube Biasing Diagram

Appendix B -- Photograph of the RCA 3RP1 Cathode Ray Tube Electron Gun

Appendix C -- Schematic diagram of the 3RP1 CRT and its pins.

Figure 1. The filament, cathode, grids and anode of the 3RP1 cathode ray tube.