The potential energy of the system of two identically charged spheres as shown in the figures is equal to (Assume the charge distribution to be uniform)

Options

A. `(q^(2))/(4piepsilon_(0))((1)/(R )+(1)/(r ))s`
B. `(1)/(4piepsilon_(0))(q^(2))/(r )`
C. `(1)/(4piepsilon_(0))(q^(2))/(r (R+r))`
D. None of these

Explanation

Each of the charged sphere will have potential energy due to its own charge or self energy
`U_(1)=(1)/(8piepsilon_(0))(q^(2))/(r )`.
The mutual potential energy stored in one sphere in the electric field of the other is `(q_(1)q_(2))/(4piepsilon_(0)r_(12))=U_(2)`
`rArr U_(2)=(1)/(4piepsilon_(0))(q^(2))/(R )`
Therefore the `P.E.` stored in the system of spheres is
`U=2U_(1)+U_(2)=(q^(2))/(4piepsilon_(0))[(1)/(R )+(1)/(r )]`
`:. (A)`