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

C

Explanation

The initial change distribution is as shown in the figure.
Initial electrostatic potential energy is

`U_(i) = - (kq^(2))/(a) + (kq^(2))/(b)-(kq^(2))/(b)+(kq^(2))/(2a)+(kq^(2))/(2b)`
`= (kq^(2))/(2b)-(kq^(2))/(2a) = (q^(2))/(8pi epsilon_(0)) [(1)/(b)-(1)/(a)]`
Final potential energy `U_(f) = 0`
`:. DeltaW = U_(f) - U_(i) = (q^(2))/(8pi epsilon_(0)) [(1)/(a)-(1)/(b)]`