Problem 3.26

A system consists of a ball of radius \(R\) carrying a spherically symmetric charge and the surrounding space filled with a charge of volume density \(\rho=\alpha / r,\) where \(\alpha\) is a constant, \(r\) is the distance from the centre of the ball. Find the ball's charge at which the magnitude of the electric field strength vector is independent of \(r\) outside the ball. How high is this strength? The permittivities of the ball and the surrounding space are assumed to be equal to unity.