(Figure 3.78) shows three thin concentric spherical shells A, B and C with initial charges on A , B, and C as 3 Q, 2Q, and -Q, respectively. The shells A amd C are connected by a wire such that it does not touch B. Shell B is earthed. Determine the final charges `q_A, q_B, "and" q_C`.
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Explanation

The first equation holds for conservation of charge on A and C
`q_A + q_C = 3Q - Q = 2Q` ...(i)
The second equation holds for zero potential of earthed surface
`(V_B)_("surface") + (V_C)_("out") + (V_A)_("in") = 0`
or `(K q_B)/(2) + (K q_C)/(2 R) + (K q_A)/(3 R)= 0`
or `(q_B)/(2) + (q _C)/(2) + (q_A)/(3) = 0` ...(ii)
Also the third equation holds for potential of A and C being equal `V_A = V_C`.
`V_A = (V_A)_("surface") + (V_B)_("out") + (V_C)_("out")`
`V_C = (V_A)_("in") + (V_B)_("in") + (V_C)_("surface")`
`:. (K q _A)/(3 R) + (K q_B)/(3 R) + (k q_C)/(3 R) = (K q_C)/(R) + (K q_B)/(2 R) + (K q _A)/(3 R)`
or `(q_A)/(3) + (q_B)/(3) + (q_C)/(3)= q_C + (q_B)/(2) + (q_A)/(3)` ...(iii)
Now on solving for `q_A, q_B`, and `q_C`, we get
`q_C = Q/(2) , q_A = (3 Q)/(2)`, and `q_B= (-3 Q)/(2)`.