Question

Using Gauss's law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point (i) outside, and (ii) inside the shell. 

Plot a graph showing variation of electric field as function of r > R and r < R (r being the distance from the centre of the shell).

Answer 1

Electric field due to a uniformly charged thin spherical shell :

(i) When point P lies outside the spherical shell : Suppose that we have to calculate electric field at the point P at a distance r (r > R) from its centre. Draw the Gaussian surface through point P so as to enclose the charged spherical shell. The Gaussian surface is a spherical shell of radius r and centre O.

(ii) When point P lies inside the spherical shell : In such a case, the Gaussian surface encloses no charge. According to the Gauss's law,