Figure shows three concentric thin spherical shells A, B and C of radii a, b and c respectively. The shells A and C are given charges q and -q respectively and the shell B is earthed. Find the charges appearing on the surfaces of B and C.

Explanation

Let total charge on middle shell be `Q`.
The potential at `P`
`V_(P) = (1)/( 4pi in_(0)) [ (q)/(b) + (Q)/( b ) + (-q)/(c )] = 0`
`Q = -q + (qb)/(c )`
Charge distribution : Since facing surfaces have equal and opposite charges , charge on inner surface of middle shell: `-q`.
The charge on outer surface of middle shell `= (qb)/(c )`
Check : Total charge on middle surface `= -q + (qb)/(c ) , O.K.`
Charge on inner surface of outer shell `= -(qb)/(c )`
Charge on outer surface of outer shell `= (qb)/(c ) - q`
Check : Total charge on outer shell `- (qb)/(c ) + ((qb)/( c) - q) = -q, O.K.`