Question

Inside a conducting hollow sphere of inner radius `R_(1)` and outer radius `R_(2)`, a point charge q is placed at a distance `x` from the center as shown in (Fig. 3.70.) Find.
.
(i) electric potential at C
(ii) electric field and potential at a distance r from the center outside the shell.

Answer 1

The electric potential at center hue to this system is due to q, induced charge -q on inner surface, and induced charge +q on outer surface. Thus,
`V_C = (K q)/(x) -(K q)/R_(1) + (K q)/R_(2)`
Electric field and potential at a distance r from the center outside the shell will only be due to the charge on outer surface because outside cavity the field due all the cavity charges is always zero. As induced charge on inner surface of cavity always nullifies the effect of point charge inside it.
`E_(out) = (K q)/(r^2) and V_(out) = (K q)/r`.