Three concentric spherical metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities `sigma`, `-sigma` and `sigma` respectively.
`(i) Find the potential of the three shells A, B and C.
(ii) If the shells A and C are at the same potential, obtain the relation between the radii a, b and c.

Options

A. `a = b + c`
B. `c = a + b`
C. `b + a + c`
D. `2a = b - c`

Answer

B

Explanation

`q_1 = sigma 4 pi a^2, q_2 = -sigma 4 pi b^2, q_3 = sigma 4 pi c^2`
`V_A = (kq_1)/a + (kq_2)/b + (kq_3)/( c)`
=`(1)/(4 pi epsilon_0)[(sigma 4 pi a^2)/a - (sigma 4 pi b^2)/b + (sigma 4pi c^2)/( c)]`
=`(sigma)/(epsilon_0)[a - b + c]`
Similarly, `V_B = (kq_1)/b + (kq_2)/b + (kq_3)/( c)`
`V_C = (kq_1)/( c) + (kq_2)/( c) + (kq_3)/( c)`
For problem `21, put V_A = V_c`.
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