Question

A uniformly charged ball of radius a and charge –Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a net charge of +2Q. Determine the strength of electric field in the four regions:

Answer 1

Answer:

i) $E = \frac{-Q r}{4\pi \epsilon_0 a^3}$

ii) $E = \frac{-Q}{4\pi \epsilon_0 r^2}$

iii) E = 0

iv) $E = \frac{Q}{4\pi \epsilon_0 r^2}$

Explanation:

1) Electric field inside uniformly charged ball

By Gauss law we will have

$\int E . dA = \frac{q_{en}}{\epsilon_0}$

now we have

$E(4\pi r^2) = \frac{-Q r^3}{\epsilon_0 a^3}$

$E = \frac{-Q r}{4\pi \epsilon_0 a^3}$

2) Electric field outside the ball and inside the shell

By Gauss law we will have

$\int E . dA = \frac{q_{en}}{\epsilon_0}$

now we have

$E(4\pi r^2) = \frac{-Q}{\epsilon_0}$

$E = \frac{-Q}{4\pi \epsilon_0 r^2}$

3)Electric field inside the metallic shell

E = 0

As we know that inside the conductor net electric field is always zero

4)Electric field outside the shell

By Gauss law we will have

$\int E . dA = \frac{q_{en}}{\epsilon_0}$

now we have

$E(4\pi r^2) = \frac{-Q + 2Q}{\epsilon_0}$

$E = \frac{Q}{4\pi \epsilon_0 r^2}$