A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q A charge q - Physics - Electrostatic Potential And Capacitance

Question

A spherical conducting shell of inner radius r1 and outer radius
r2 has a charge Q A charge q is placed at the centre of the
cell
(a) What is the surface charge density on the (i) inner surface
(ii) outer surface of the shell
(b) Write the expression for electric field at a point x r2 from
the centre of the shell

Himanshu · Accepted Answer

Surface charge density on the inner surface is $\frac{q}{4 π R_{1}^{2}}$

Surface charge density on the outer surface is $\frac{Q + q}{4 π R_{2}^{2}}$

For finding the electric field at a distance x from the center, we need to apply Gauss's law.

$E \times 4 π x^{2} = 4 π Q_{e n c l o s e d} = 4 π (Q + q) E = \frac{(Q + q)}{x^{2}}$