A point charge 'Q' is placed at the centre of a spherical cavity of radius 'b' carved inside a solid conducting sphere of radius 'a'. Then total energy of the system is:
`[k = (1)/(4pi in_(0))]`

Options

A. `(KQ^(2))/(2a) - (kQ^(2))/(2b)`
B. `(kQ^(2))/(2a) + (kQ^(2))/(2b)`
C. `(kQ^(2))/(a) + (kq^(2))/(b)`
D. `(kQ^(2))/(a) - (kQ^(2))/(b)`

Answer

A

Explanation

`-Q` and `Q` will be induced uniformly as shown.
Total energy `=` Self-energy `+` interaction energy
`= (k(-Q)^(2))/(2b) + (k(Q)^(2))/(2a) +(k(Q)(-Q))/(b) + (k(Q)(+Q))/(a) +(k(Q)(-Q))/(a)`
`= kQ^(2) ((1)/(2a)-(1)/(2b))`