Question

A point charge `q` is located at the centre `O` of a spherical uncharged coducting layer provided with small orifice. The inside and outside radii of the layer are equal to a and `b` respectively. The amount of work that has to be performed to slowly transfer the charge `q` from teh point `O` through the orifice and into infinity is

Answer 1

Correct Answer - `(q^2)/(8 pi epsilon_0) ((1)/a - (1)/b)`
Potential at center O due to induced charges is
`V_1 = - q/(4 pi epsilon_0 a) + q/(4 pi epsilon_0 b)`
`V_(oo)=0`
small work done to transfer a small charge dq from center to infinity is
`d W = d q (V_oo - V_1) = (1)/(4 pi epsilon_0) [(1)/a - (1)/b] q d q`
or `W = int d W = (q^2)/(8 pi epsilon_0) [(1)/a - (1)/b]`.