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.

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

A system consits of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density rho=alpha/r , where alpha is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

A solid sphere of radius R has a charge Q distributed in its volume with a charge density rho=kr^a , where k and a are constants and r is the distance from its centre. If the electric field at r=(R)/(2) is 1/8 times that r=R , find the value of a.