A charge Q is distributed over three concentric spherical shells of radii a, b, c (a`lt` b `lt` c) such that their surface charge densities are equal to one another.
The total potential at a point at distance r from their common centre, where r`lt`a, would be :

Options

A. `(Q(a+b+c) )/(2pi epsi_0 (a^2 + b^2 + c^2) )`
B. `(Q)/(4pi epsi_0 (a + b +c) ) `
C. `(Q)/(12 pi epsi_0) (ab + bc + ca)/(abc)`
D. `(Q (a^2 + b^2 + c^2) )/(4 pi espi_0 (a^3 +b^3 + c^3) )`

Answer

A

Explanation

` (q_1)/(a^2) = (q_2)/(b^2) = (q_3)/(c^2) = k` (constant) ` to k (a^2 + b^2 + c^2) = 2Q`
` V(r ) = (1)/(4pi epsi_0) ((q_1)/(a) + (q_2)/(b) + (q_3)/(c ) )`
` = (1)/(4pi epsi_0) (ka + kb + kc) = (1)/(4pi epsi_0) xx ( 2Q)/((a^2 + b^2 + c^2) ) (a+b+c) `
` = (Q)/(2 pi espi_0) ((a+b+c)/(a^2+b^2+c^2))`