Two concentric conducting spherical shells of radii `a_1 and a_2 (a_2 gt a_1)` are charged to potentials `phi_1` and `phi_2`, respectively. Find the charge on the inner shell.

Options

A. `q_1 = 4 pi epsilon_0 ((phi_1 - phi_2)/(a_2 - a_1)) a_1 a_2`
B. `q_1 = 4 pi epsilon_0 ((phi_1 + phi_2)/(a_2 + a_1)) a_1 a_2`
C. `q_1 = pi epsilon_0 ((phi_1 - phi_2)/(a_2 + a_1)) a_1 a_2`
D. `q_1 = 2 pi epsilon_0 ((phi_1 + phi_2)/(a_2 - a_1)) a_1 a_2`

Answer

a

Explanation

`phi_1 = (k q_1)/(a_1) + (k q_2)/(a_2)`
or `phi_2 = (k q_1)/(a_2) + (k q_2)/(a_2)`
Solve to get
`q_1 = (1)/(4 pin epsilon_0)[(phi_1 - phi_2)/(a_2 - a_1)] a_1 a_2`
.