Problem 3.25

A ball of radius $R$ carries a positive charge whose volume density depends only on a separation $r$ from the ball's centre as $\rho=\rho_{0}(1-r / R),$ where $\rho_{0}$ 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 $E_{\max }$ and the correspond ing distance $r_{m}$.