Question

figure shows 3 concentric spherical shells A, B and C with initial charges on A, B and C as 3q, 2q and - q respectively. The shells A and C are connected by a wire such that it doesn't touches B. Shell B is earthed. determine the final charges on A, B and C

Please answer with explanation.
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Answer 1

The first equation holds for conservation of charge on A and C

qA+qC= 3q-q= 2q. --------(1)

The second equation holds for zero potential of earthed surface

Vb(surface)+Vc(out)+Va(in) = 0

$\frac{qb}{2} + \frac{qc}{2} + \frac{qa}{3} = 0 - - - - - - (2)$

also the third equation holds for potential of A and C being equal

Va= Vc

Va= Va(surface)+Vb(out)+Vc(out)

Vc= Va(in)+Vb(in)+Vc(surface)

$\frac{qa}{3} + \frac{qb}{3} + \frac{qc}{3} - - - - - (3)$

now solving for qa,qb and qc

$qc= \frac{q}{2} \\ qa = \frac{3q}{2} \\ qb = \frac{ - 3q}{2}$