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Q.

Two concentric, conducting, thin spherical shells A and B have radii r and R as shown in fig. Shell A carries a charge q and B carries a charge Q. Shell A is supported on an insulating stand. The potential of shell A is

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a

$\frac{1}{4 π ε_{0}} \frac{q}{r}$

b

$\frac{1}{4 π ε_{0}} (\frac{q}{r} + \frac{Q}{R})$

c

$\frac{1}{4 π ε_{0}} (\frac{Q}{r} + \frac{q}{R})$

d

$\frac{1}{4 π ε_{0}} (\frac{q + Q}{R - r})$

answer is A.

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Detailed Solution

For any point inside a shell, potential due to a charge Q distributed on the surface of the shell is given by

$V = \frac{Q}{4 π ε_{0} R}$

Therefore potential on the inner shell surface will be

$V_{A} = \frac{q}{4 π ε_{0} r} + \frac{Q}{4 π ε_{0} R}$

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Two concentric, conducting, thin spherical shells A and B have radii r and R as shown in fig. Shell A carries a charge q and B carries a charge Q. Shell A is supported on an insulating stand. The potential of shell A is