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

i)
`E = (-Q r)/(4\pi \epsilon_0 a^3)`

ii)
`E = (-Q)/(4\pi \epsilon_0 r^2)`

iii) E = 0

iv)
`E = (Q)/(4\pi \epsilon_0 r^2)`

Step-by-step explanation:

1) Electric field inside uniformly charged ball

By Gauss law we will have

`\int E . dA = (q_(en))/(\epsilon_0)`

now we have

`E(4\pi r^2) = (-Q r^3)/(\epsilon_0 a^3)`

`E = (-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 = (q_(en))/(\epsilon_0)`

now we have

`E(4\pi r^2) = (-Q)/(\epsilon_0)`

`E = (-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 = (q_(en))/(\epsilon_0)`

now we have

`E(4\pi r^2) = (-Q + 2Q)/(\epsilon_0)`

`E = (Q)/(4\pi \epsilon_0 r^2)`