A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density p (r) is given by

Here a is a positive constant having units of C/m3 €¢
(a) Determine a in terms of Q and R.
(b) Using Gauss's law, derive an expression for the magnitude of E as a function of r. Do this separately for all three regions. Express your answers in terms of the total charge Q.
Be sure to check that your results agree on the boundaries of the regions.
(e) What is the period of the motion in part (d)? (i) If the amplitude of the motion described in part (e) is greater than R/2, is the motion still simple harmonic? Why or why not?

Transcribed Image Text:

for rS R2 p(r) = a p(r) = 2a(1 - r|R) for R/2 srSR p(r) = 0 for r2 R