Question

Hi could you please help me on this.
1. when point charge is placed inside hollow spherical conductor and outside surface of the spherical conductor is grounded. then how do the charges distribute in inner surface? what is the electric field of all the region?
2. when point charge is placed off from the center what is the charge density at inner surface? and what is the electric field in all the regions?

Answer 1

When the outside surface of a conductor is grounded then this surface will be discharged. The net charge of the system will be zero. Distribution of charge in inner surface depends of the position of charge inside the conductor. In the simplest case where the point charge is in the center of a sphere the electric field if r<R is simply
\[\frac{ Q }{ 4\pi \epsilon_{0} r^{2} }\]
The electric field when r>R and, of course, inside the conductor is zero.
When point charged is placed off then the conductor will be charged. The charge will distribute itself uniformly with the charge density
\[\sigma = \frac{ Q }{ 4\pi R^{2} }\]
but on the outer surface.
The electric field is then only on the outside, equal in the magnitude with the first equation above. There is no charge density on the inner surface.

Answer 2

Gauss's Law