A metallic spherical shell has an inner radius R₁ and outer radius R₂. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?

Question

A metallic spherical shell has an inner radius R₁ and outer radius R₂. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?

Philoid · Accepted Answer

Since the spherical shell with an inner radius R₁ and an outer radius R₂ is metallic, there are free electrons in the shell. The positive charge Q is placed at the centre of the spherical shell as shown in the figure below.

The charge Q will cause equivalent negative charge -Q to be induced on the inner surface while there is equivalent positive charge +Q induced on the outer surface.

Surface charge density is given by

Therefore, Surface charge density on the inner surface is

Surface charge density on the outer surface is

A metallic spherical shell has an inner radius R1 and outer radius R2. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?

A metallic spherical shell has an inner radius R₁ and outer radius R₂. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?