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

As shown in the previous worked out example, the inner surface of B must have a charge -q from the Gauss's law. Suppose, the outer surface of B has a charge q'. The inner surface of c must have a charge -q' from the Gauss's law. As the net charge on C must be -q, its outer surface should have a charge q'-q. The charge distribution is shown in figure (30-W2b).
The potential at B dut to the charge q on A
`=q/4phiepsilon_0b`,
due to the charge -q on the inner surface of B
`=-q/4phiepsilon_0b`,
due to the charge q' on the outer surface of B
`= q'/4phiepsilon_0 b`,
due to the charge -q', on the inner surface of c
`=-q'/4phiepsilon_0 c
and due to the charge q' -q on the outer surface of C
`= q'-q/4phi epsilon_0 C`.
The net potential is
`V^B=q'/4phi epsilon_0 b- q/ 4phi epsilon_0 c`.
This should be zero as the shell B is earthed. Thus,
`q'=b/c q. The charge on various surface are as shown in figure