In the following, ignore the gravitational force on the particle.

Do the following problems in the corresponding WebAssign assessment.

1. Click here to open an IWP applet.  A proton is in a magnetic field that points out of the screen (+z) and an electric field that points in the +y direction.  As in previous animations, the red vector is the particle's velocity, and the blue vector is its acceleration.  At t = 0 (assume the particle is moving initially), what are the directions of the electric and magnetic forces on the particle?

2. Which of the two forces is greater at t = 0, and how can you tell (even before you run the animation)?

3. Run the animation now.  Note that the acceleration vector doesn't remain perpendicular to the path as you saw in M10b when the only force acting was magnetic. Step the animation to a time of 2.55E-7 s. What are the directions of the electric and magnetic forces at this time?

4. At any point along the path, the ratio of the magnitudes of the magnetic force to the electric force is qvBsinθ/qE = vB/E (θ = 90°). Calculate the direction of the acceleration vector at t = 2.55E-7 s. Give your answer as an angle to the nearest degree measured counterclockwise from the +x axis.

5. You should be able to see now why the particle loops back on itself.  As the particle approaches the bottom of the first loop (t = 3.15E-7 s), it slows and the radius of curvature of its path decreases (remember r = mv/qB from M10b?).  It bends sharply back to the right, unable to complete a circular path.  This is the influence of the electric field.  At the bottom of a loop, the acceleration and velocity vectors are perpendicular again.  What are the directions of the electric and magnetic forces at this point? How does the magnitude of the magnitude force at this point compare to the magnitude at t = 0?

6. Increase the electric field to 8000 N/C without changing anything else. Note how the loops get tighter. Now try an electric field of 10,000 N/C.  The loops disappear entirely as the particle actually comes to a momentary stop.  What are the magnitudes of the electric and magnetic forces at this point?

7. Determine what the magnitude of the electric field must be in order for the particle to move at constant velocity. Show a complete net force solution in symbols. You'll enter a numerical value in the next problem.

8. Substitute values from the animation and calculate the electric field needed for constant velocity motion. Enter that value in the animation and test it.

9. Suppose the particle were an electron but all else remained the same from step 8? The charge would be negative, and the mass would be much smaller. What would be the directions of the forces on the electron?

10. In the applet, change the charge and mass to that of an electron and run the animation. Compare the motion to what you observed previously for a proton. Be as specific as possible. Explain what you observed.

11. Change the particle to an alpha particle. This is a Helium-4 nucleus and is composed of 2 protons and 2 neutrons. You can look up the mass in Appendix F. (This is the mass of the entire atom, but it's close enough, since the electrons are much less massive than the nucleus.) The units are atomic mass units. Get the conversion factor from the inside back cover. Make sure you're still using the value of electric field that makes the particle move at constant velocity. Now reverse the direction of the velocity (change the angle to 180°). What are the directions of the electric and magnetic forces on the alpha particle?

12. What combinations of E- and B-field directions will result in the alpha particle moving at constant velocity to the left?