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2. Relevant equations

3. The attempt at a solution

Potential at the center of conducting charged sphere surrounded by a grounded shell

If I take another sphere of charge –q of radius a with uniform charge density, then the potential on the spherical region from the radius a to b is same to that of the original question.

According to Uniqueness theorem, the V at the center of the sphere due to the above system should be equal to that of the original question.

Since the conducting sphere is an equipotential, the potential due to this sphere at center is same to that of the surface = ## \frac { q}{4 \pi \epsilon _0 R} ## .

The potential due to the image sphere of charge –q at the center is ## \frac { -q}{4 \pi \epsilon _0 a} ## .

So, the total potential at the center is ## \frac { q}{4 \pi \epsilon _0 R} ## - ## \frac { q}{4 \pi \epsilon _0 a} ## , option (d).

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# Homework Help: V(center) of charged metal sphere inside a grounded shell

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