A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball's centre as P = P0 (1 – r/R), where P0 is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find:
(a) The magnitude of the electric field strength as a function of the distance r both inside and outside the ball;
(b) The maximum intensity Emax and the corresponding distance rm.