Question

A spherical conducting shell of inner radius r₁ and outer r₂ has a charge Q. 

(a) A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surface of the shell. 

(b) Is the electric filed inside a cavity (with no charge) zero; independent of the fact whether the shell is spherical or not? Explain. 

Answer 1

(a) The charge + Q resides on the outer surface of the shell. As the charge q is placed at the centre of the shell, there is charge –q induced on the inner surface and a charge + q is induced on the outer surface of the shell. Thus, the total charge on the inner surface of the shell is – q and on the outer surface of the shell is (Q+ q). 

The surface charge density on the inner surface 

The surface charge density on the outer surface 

(b) Yes, the electric field inside a cavity is zero, if the shape of the shell is not spherical. If we take a closed – loop which is inside the cavity along a field line and the rest outside it, the net work done by the field in carrying a test charge over the closed – loop will not be zero. So, the electric field inside a cavity with no charge is always zero.