Question

A sphere of radius $0.03$ m is suspended within a hollow sphere of radius $0.05$m. If the inner sphere is charged to a potential of $1500$ volt and outer sphere is earthed, find the capacitance and the charge on the inner sphere.

Answer 1

Potential on outer surface:

$\frac{K{Q}_1}{0.05}+\frac{K{Q}_2}{0.05}=0$

$\Rightarrow Q_1=-Q_2$

Potential on inner surface:

$\frac{K{Q}_1}{0.03}-\frac{K{Q}_2}{0.05}=1500$

$Q_1=\frac{1500\times 15\times {10}^{-2}}{2\times 9\times {10}^9}$

$=12.5\times {10}^{-9}C$

$C=\frac{Q}{V}=\frac{12.5\times {10}^{-9}}{1500}=8.33\times {10}^{-12}F$