L23. Charge-to-Mass Ratio of Electrons

Goals:  1) to develop the theory for methods of measuring the charge-to-mass ratio of electrons, and 2) to collect data from photographs and use that data together with the theory to calculate the charge-to-mass ratio.

About completing this lab: You must complete the Theory and Design before continuing below.

Data and Analysis

What to submit: If you've completed and submitted all three cases of Theory and Design, you may continue with the following. You'll submit a Word document as your lab report. Provide the customary heading. Label the successive sections of your report as they're labeled below. Name your Word file L23-WAusername.doc.

Information about the photos is given here. Go ahead and click on Photo 24. Be sure that the photo opens to full size in your browser window. The trajectory is that due to the electric field set up by potential V2 across the metal plates at the top and bottom of the grid. The grid is ruled in minor divisions of 0.002 m and major divisions of 0.01 m. It's a bit difficult to see the grid on the left side where the beam enters the field. However, you should be able to make readings to the nearest millimeter (half of a minor division). The initial trajectory is along the x-axis, which runs horizontally along the center of the grid. Assume that the left edge of the grid is at x = 0.005 m. This accounts for the fact that the beam actually enters the field about half a centimeter before it reaches the grid.  In some photos, you'll see a second fainter blue line. Ignore that one and use the brighter line for measurements. Here's some more information you'll need.

The spacing d between the plates that produce the electric field is 0.060 m. We're giving you the value, because the top and bottom edges of the grid are partially obscured.

When there's a coil current, I,  there will be a magnetic field that produces a downward magnetic force to oppose the electric force. The magnitude of the magnetic field is calculated using this formula:

B = (0.00411 T/A)∙I

While you can print photos for analysis, it's also possible just to read directly from the screen. As you collect data, present and organize it clearly. Include all data necessary for your calculations of q/m. This includes the ID of the photo as well as the information provided you on potential differences and current. Now do the following. Have your Theory and Design (T&D) problems handy, because you'll need to refer to that work.

Case 1. Electric field only

  1. Examine in turn each of the three photos for this case.  Look at the photo data to compare the potentials for the three photos. Why is the path of the electrons independent of the accelerating potential? In order to answer this, start with an equation from the T&D. Based upon this theory, what is the expected equation of the electron trajectory? Give your answer in reduced form.

  2. We're not going to dwell on the analysis of these photos, since they can't be used to determine q/m. However, a quick check of the theoretical equation is in order. Suppose x = 0.080 m. Use your simplified formula from step 1 to calculate the corresponding value of y. Then, for any of the three photos, read the y-coordinate of the beam at x = 0.080 m. Remember, the grid starts at 0.005 m on the left. Compare the theoretical and measured values of y. (As always, comparing two values has a specific meaning, but that can depend on context. One method of comparison is simply to find a ratio. When comparing theoretical and experimental values, however, find the experimental error.) Present your work clearly.

  3. Without having manipulated the equipment yourself, you may find it a bit difficult to identify possible sources of error. However, do your best to come up with at least one possible error. Better yet, come up with two. Here's a hint. The theory that you derived makes an assumption about the electric field. How well do you expect the actual field between the plates to fit that assumption?

Case 2. Magnetic field only

  1. Four photos are provided. They have different values of accelerating potential and current. There is no plate potential; hence, circular trajectories are expected. Select a pair of photos. Select either 18 and 19 or 20 and 21. For each photo of your pair, read the (x,y) coordinate measurements that you'll need to calculate the radius of the path. You may use (0,0) as a point even though it occurs to the left of the grid about half a centimeter.

  2. Examine the methods described in the Moodle wikis for finding the radius of the path. Select the method that you think is the best (you may select your own) and tell here why you think it's the best.

  3. Carry out your calculations of q/m for the two photos. This includes calculations of the radius (using the method selected in step 2), the magnetic field, and finally of q/m. Show one complete sample calculation. Summarize all results in a table.

  4. Calculate the accepted value of q/m using the known values for charge and mass of the electron.

  5. Compare your average value of q/m obtained from the photos to the accepted value.

  6. Once again, do your best to come up with a couple of sources of error. The hint given in Case 1 can also apply to the magnetic field of the coils.

Case 3. Crossed electric and magnetic fields

  1. Five photos taken for this situation are provided. In all cases, the electric force is up and the magnetic force is down. You're looking for the photo for which the forces are as nearly equal as possible. Hence, you're looking for a trajectory along the x-axis. You won't find an exact match due to limitations of the apparatus. However, look at each of the photos in turn and determine which one comes closest. List the data for that photo.

  2. Use the appropriate equation from the T&D to calculate q/m using the data from the photo.

  3. Compare your calculated value to the accepted value. We won't ask you to discuss sources of error this time. The sources that contribute to error for Cases 1 and 2 will of course contribute to Case 3 as well.

Conclusion

Wrap up your report by summarizing your results. Provide a comparative discussion of the Case 2 and 3 methods and evaluate which method you consider to be the better and why.