Question

A point charge is placed inside a neutral conducting sphere inner radius 2r, outer rasiud 3r

Answer 1

There are three types of charges contributing to the field at point P

The charge q itself

The induced charge on the inside of the sphere

The induced charge on the outside of the sphere.

First, the contribution due to the charge q itself will have a magnitude of kqr2=kq(4R)2+(1R)2=kq17R2kqr2=kq(4R)2+(1R)2=kq17R2

Second, the field due to the induced charge on the inside of the sphere will cancel the field of the original charge and therefore have a magnitude which is equal but opposite to the field of the original charge.

Third, if the sphere is uncharged, i.e. electrically neutral, the accumulation of charge on the inside surface, will lead to an equally large, but opposite accumulation of charge on the outside surface. This charge will be evenly spread over the surface of the sphere. The magnitude of this field is kqr2=kq16R2