Question

A spherical-shaped capacitor has a charge equivalent to 4.45 nanocoulombs when connected to a battery that has a voltage of 220 V. Suppose the two shells of the spherical capacitor are 5.34 centimeters apart, what are the capacitance and the radius of the inner sphere?

Answer 1

The capacitance is given by

$$C=\frac{q}{V}=\frac{4.45*10^{-9}}{220}=2.02*10^{-11}\:\rm F$$

On the other hand

$$C=4\pi\epsilon_0(R_2*R_1)/(R_2-R_1)$$ $$R_2=R_1+0.0534$$

So

$$2.02*10^{-11}=3.14*8.85*10^{-12}\frac{(R_1+0.0534)R_1}{0.0534}$$

$$(R_1+0.0534)R_1=0.0389$$

$$R_1=0.172\:\rm m$$

$$R_2=0.226\:\rm m$$