Two spherical conductors A and B of radii a and b (b > o) are placed con-centrically in air as shown in fig. B is given a charge + Q and A is earthed. The equivalent capacitance of the system is

 

The charge Q given to outer sphere is distributed as e outside and Q₂ inside. The inside charge Q₂ induces a charge - Q₂ on outside of inner sphere and + Q₂ on inside
of inner sphere which is earthed. The inside of outer sphere and outside of inner sphere constitute a spherical condenser having capacitance $\left[4{\mathrm{\pi \epsilon }}_0\{\mathrm{ab}/(\mathrm{b}-\mathrm{a}\left)\right\}\right]$ and
the outside of the outer constitutes an isolated sphere of capacitance $4{\mathrm{\pi \epsilon }}_0\mathrm{b}$.
Now the effective capacitance C is given by
$\begin{array}{l}\mathrm{C}=4{\mathrm{\pi \epsilon }}_0\left\{\frac{\mathrm{ab}}{(\mathrm{b}-\mathrm{a})}\right\}+4{\mathrm{\pi \epsilon }}_0\mathrm{b}\\ =4{\mathrm{\pi \epsilon }}_0\mathrm{b}\left[\frac{\mathrm{a}}{(\mathrm{b}-\mathrm{a})}+1\right]\\ =4{\mathrm{\pi \epsilon }}_0\mathrm{b}\left[\frac{\mathrm{a}+\mathrm{b}-\mathrm{a}}{(\mathrm{b}-\mathrm{a})}\right]\\ =4{\mathrm{\pi \epsilon }}_0\left\{\frac{{\mathrm{b}}^2}{(\mathrm{b}-\mathrm{a})}\right]\end{array}$