Question

A point charge q is placed inside a conducting spherical shell of inner radius 2r and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be 1/4𣕠times

Answer 1

The charge q put inside the shell causes an instigated charge −q on the inward surface of the shell and +q charge on the external surface. The potential at the middle is presently because of (I) charge q put inside the shell (ii) charge −q on the internal surface of the shell and (iii) charge +q on the external surface of the shell. Since the shell is thin, its internal and external radii can be viewed as equivalent - each equivalent to R.  

V=14πϵoqr−14πϵoqR+14πϵoqR=14πϵoqr  

3. On the off chance that it is a shell having inward and external radii Ri and Ro individually (however it has not been inquired):  

As clarified above in point (2) the potential at the inside is because of (I) given charge q at a separation r from the middle (ii) −q incited on the internal surface of sweep Ri and (iii) +q actuated at the external surface of span Ro.  

V=14πϵoqr−14πϵoqRi+14πϵoqRo=q4πϵo(1r−1Ri+1Ro)