Student Worksheet

1. Run the simulation. You can click-drag in the window to rotate the view and shift-click to zoom in and out. The plot (that opens in a second window) shows the x-component of position (blue) and velocity (red) of the yellow test charge as a function of time. The convention is that a test charge is positive, but of small enough size so that its own electric field can be neglected. Therefore, the simulation only shows the electric field due to the green charges. Are the green charges positive or negative? Explain.
2. Change the radius of the ring of green charges and observe the motion. Why does the test charge stay on the x-axis?
3. If you Pause the simulation and move the charge slightly off-axis, what happens? Why?
4. Reset the simulation and run it with the initial parameters (test charge on the x-axis and a ring radius of 8 cm). Look at the data plot. What is the period of oscillation?
5. Explain why, for larger values of the ring radius and motion near the ring, the motion is sinusoidal (it looks like simple harmonic motion). Hint: Start with the equation of the electric field on axis of a ring of charge and compare it to the the force for simple harmonic motion. Show that the frequency of oscillation (of this simple harmonic oscillator) is equal to ?=(qQ/4??₀mR³)^1/2 where q is the charge of the test charge, Q, the magnitude of the total charge on the ring and R, the radius of the ring. Therefore, if the total charge on the ring is one million times the charge of the test charge and the test charge has a mass of 1 ?g (=10^-9 kg), what is the magnitude of the green and yellow charges?