Question

An insulating sphere of radius 4.0 cm has a total charge of 4.0 * 10 ^ - 9 C distributed uniformly over its volume. Find (a) its volume charge density and (b) the potential at its surface.

Answer 1

Given:

$R=0.04\:\rm m$

$q=4.0*10^{-9}\: \rm C$

(a) the volume charge density

$$\rho=\frac{q}{V}=\frac{q}{4/3\pi R^3}\\ =\frac{4.0*10^{-9}}{4/3*3.14*0.04^3}=1.5*10^{-5}\rm C/m^3$$

(b) the potential

$$V=k\frac{q}{R}=9*10^9*\frac{4.0*10^{-9}}{0.04}=900\:\rm V$$