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

Explanation

Initally, there will be induced charges of magnitude `-q` and `+q` on the inner and outer surface of the spherical layer respectively. Hence, the total electrical energy of the system is the sum of self energies of spherical shells, having radii `a` and `b`, and their mutal energies including the point charge `q`.
`U_(i) = (1)/(2) (q^(2))/(4pi epsilon_(0) b) + (1)/(2) ((-q)^(2))/(4pi epsilon_(0) a) + (-q q)/(4pi epsilon_(0) a) + (qq)/(4pi epsilon_(0) b) + (-qq)/(4pi epsilon_(0) b)`
or `U_(i) = (q^(2))/(8pi epsilon_(0)) [(1)/(b) - (1)/(a)]`
Finally, charge `q` is at infinity hence, `U_(f) = 0`
Now, work done by the great = increment in the energy
`= U_(f) - U_(i) = (q^(2))/(8pi epsilon_(0)) [(1)/(a) - (1)/(b)]`