Question

A point charge +Q is placed at the center O of an uncharged hollow spherical conductor of inner radius 'a' and outer radius 'b'. Find the following:

(a) The magnitiude and sign of the charge induced on the inner and outer surface of the conducting shell.

(b) The magnitude of electric field vector at a distance

(i) r = \(\frac{a}{2}\), and

(ii) r = 2b, from the center of the shell.

Answer 1

(a) The charge on the inner durface of the conducting shell = -Q

The charge on the outer surface of the conducting shell = +Q

(b) (i) For r = \(\frac{a}{2}\)

E = \(\frac{1}{4\piɛ_o} \frac{Q}{r^2} = \frac{1}{4\piɛ_o} \frac{4Q}{a^2}\)

(ii) For r = 2b

E = \(\frac{1}{4\piɛ_o} \frac{Q}{r^2} = \frac{1}{4\piɛ_o} \frac{Q}{4b^2}\)