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. Asumming the permittivites of the ball and the enviroment 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 corresponding distance `r _(m)`.

Answer

(i) `E=(rho_(0)r)/(3 epsi_(0)) (1-(3r)/(4R))` for `r lt R, E=(rho_(0)R^(3))/(12 epsi_(0) r^(2))` for `r gt R` (ii) `E_("max")=1/9 (rho_(0)R)/epsi_(0)` for `r_(m)=2/3 R`.