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.

Answer 1

We have,

$radii=r_1,r_2$

$charge=Q,q$

So,

a) Surface charge density on the inner surface is:

$\frac{q}{4\pi r_1^2}$

Surface charge density on the outer surface is:

$\frac{q+Q}{4\pi r_2^2}$from

b) For finding the electric field at the distance x from the center is:

For this Apply the Gauss law,

$E\times 4\pi x^2=4\pi (Q+q)$

$E=\frac{Q+q}{x^2}$