Question

A dielectric ball is polarized uniformly and statically. Its polarization equals P. Taking into account that a ball polarized in this way may be represented as a result of a small shift of all positive charges of the dielectric relative to all negative charges, 

(a) find the electric field strength E inside the ball; 

(b) demonstrate that the field outside the ball is that of a dipole located at the centre of the ball, the potential of that field being equal to φ = p₀r/4πε₀, where P₀ is the electric moment of the ball, and r is the distance from its centre.

Answer 1

In a uniformly charged sphere,

where  (dipole moment is defined with its direction being from the -e charge to +ve charge.) 

The potential outside is