Question

3. A solid conducting sphere of radius b carries a net charge of -Q. Select the correct option on the right panel, for the electric potential V(r) at a radial distance of ( b/2 ) from the center of the sphere, with respect to the potential of the sphere at infinity.

Answer 1

We here have a conducting sphere of radius b with -Q charge and we have to find out the potential at b/2 from the middle of the sphere ie potenital inside the sphere.

For a conducting sphere, when given any charge, the charges will rearrange themselves in such a way that all the charges will be present at the surface of the sphere and a layer of oppostitely charged charges will be present in the layers inside to maintain charge conservation and as a result of this the electric field produced by the charge on the sphere will be cancelled by the charges induced inside the sphere and as resut of this the electric field inside the sphere would be zero. Or if you apply Gauss' law inside the sphere, you will find that the electric field inside the sphere is zero since the enclosed charge is zero(there are equal number of positive and negative charges). Therefore we can conclude that electric field is only present outside the sphere and that is given by,

The potential as b/s is given by,

Since E(r) in the limit b to b/2 is zero:

ie,

Applying the limits,