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

$\frac{1}{4 \pi \varepsilon_0}\left[\frac{1}{R}+\frac{1}{r}\right]$

Each of the charged sphere will have potential energy due to its own charge

$U_1=\frac{1}{8 \pi \varepsilon_0} \frac{q^2}{r}$

The potential energy stored in one sphere due to the potential of the other is

$U_2=\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{R}$

Therefore the P.E. stored in the system of spheres is

U = U₁ + U₂

$=\frac{1}{4 \pi \varepsilon_0}\left[\frac{1}{R}+\frac{1}{r}\right]$

∴ (A)