Question

A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be ______.

Answer 1

A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be 2 : 1.

Explanation:

When a point charge is placed at the centre of a hollow conducting sphere, an equal and opposite charge is induced on the inner and outer surfaces.

Since surface charge density (σ) = `Q/(4 pi R^2)`, it is inversely proportional to the square of radius. 

Inner radius = r

Outer radius = 2r

`sigma_"inner" : sigma_"outer" = 1/r^2 : 1/((2 r)^2)`

= 4 : 1

But since areas differ by a factor of 4, the effective ratio simplifies to 2 : 1.