Question

1. A solid conducting sphere of radius 40 cm has a charge of 5 µC. If the potential is zero

at infinity. Find the value of the potential at the following distances from the center of

the sphere:

a) 50 cm b) 40 cm c) 25 cm

Answer 1

$\varphi= \begin{cases} \frac 32\frac{kq}{R}- \frac{kqr^2}{2R^3}&\text{if } r<R, \\ \frac{kq}{r}&\text{if } r≥R; \end{cases}$

a)

$\varphi=\frac{9\cdot 10^9\cdot 5\cdot 10^{-6}}{0.5}=90~kV,$

b)

$\varphi=\frac{9\cdot 10^9\cdot 5\cdot 10^{-6}}{0.4}=112.5~kV,$

c)

$\varphi=\frac 32\cdot \frac{9\cdot 10^9\cdot 5\cdot 10^{-6}}{0.4} -\frac{9\cdot 10^9\cdot 5\cdot 10^{-6}\cdot 0.25^2}{2\cdot 0.4^3}= 146.8~kV.$