A system consists of a ball of radius R carrying a uniformly distributed charge q and the surrounding space filled with a charge of volume density `rho = alpha//r`, where `alpha` is a constant and r is the distance from the centre of the ball. Find the charge on the ball for which the magnitude of electric field strength outside the ball is constant? The dielectric constant of the ball and the surrounding may be taken equal to unity.

Answer

`q=2 pi alpha R^(2), E=1/2 alpha/epsi_(0)`