There is a point charge +q inside a hollow sphere and a point charge -q just outside its surface. The total flux passing through the surface of sphere is :

Options

A. If the magnitude of charge on sphere is more than that of point charge then there will be positive charge on the outer surface and negative on the inner surface of hollow sphere.
B. If The magnitude of charge on sphere is more than that of point charge then there will be positive charge on the outer surface and inner surface of hollow sphere
C. If the magnitude of charge on sphere is less than that of point charge then there will be negative charge on the outer surface and positive charge on the inner surface of hollow sphere.
D. If the magnitude of charge on sphere is less than that of point charge then there will be negative charge on the outer surface and inner surface of hollow sphere

Answer

B, C

Explanation

First of all, let us understand how the charge is induced on the sphere due to presence of charge at the centre.
Charge kept at the centre of sphere is-q. We are aware that whatever charge we bring near the metal object, it induces equal and opposite charge on the surface of metal near it and a charge of the same magnitudc but of opposite polarity on farther surface of metal object. Charge induced on the inner surface of sphere must be +q and it should be Q -q on the outer surface The sphere is isolated, hence, its net charge cannot change. The sum of the charges on inner and outer surfaces must remain equal to +Q because induction of charge does not change the net charge. Charge on the outer surface of sphere is Q- q, for Q>q the outer surface acquires net positive charge. But we know that inner surface has positive charge for sure. Hence option (a) is not correct or rather it is only partially corre( but option (b) is fully correct. Charge on outer surface of sphere is Q-q, hence for Q< q the outer surface acquires net negative charge. But we know that the inner surface has a positive charge for sure. Hence option (c) is correct. Option (d) is not correct because there is a positive charge for sure on the inner surface of sphere