Question

A sphere of radius r carries a surface charge of density σ = ar, where a is a constant vector, and r is the radius vector of a point of the sphere relative to its centre. Find the electric field strength vector at the centre of the sphere.

Answer 1

Given charge distribution on the surface  is shown in the figure. Symmetry of this distribution implies that the sought  at the centre O of the sphere is opposite to vector a. 

Again from symmetry, field strength due to any ring element vector dE is also opposite to

Comments

Nice!