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 the electric field as a function of r. Do this separately for all three regions. Express your answers in terms of the total charge Q.

Transcribed Image Text:

p(r) = 3ar|(2R) for r= R/2 P(r) = o[1 - (r/R)²] for R/2