A point charge q is held at distance r from the centre of a neutral conducting sphere of radius R (r R). Consider a point P inside the sphere located at distance r1 from the point charge q. The potential at P due only to the induced charges on the sphere is:

Question

A point charge q is held at distance r from the centre of a neutral conducting sphere of radius R (r > R). Consider a point P inside the sphere located at distance r1 from the point charge q. The potential at P due only to the induced charges on the sphere is:

Accepted Answer

Kq/r - Kq/r1. A conductor is an equipotential; inside it the total potential is constant and equals the potential at its centre, where the point charge contributes Kq/r and the induced charges contribute zero (they sum to zero net charge and centre is equidistant in the net-zero sense), giving V_total = Kq/r. At point P the point charge q alone contributes Kq/r1. Since V_total = V_q + V_induced, the induced part is V_induced = V_total - V_q = Kq/r - Kq/r1.

A point charge q is held at distance r from the centre of a neutral conducting sphere of radius R (r > R). Consider a point P inside the sphere located at distance r1 from the point charge q. The potential at P due only to the induced charges on the sphere is:

Solution

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