Question

The point charge $q$ is within the cavity of an electrically neutral conducting shell whose outer surface has spherical shape. Find the potential $V$ at a point P lying outside the shell at a distance $r$ from the center $O$ of the outer sphere.

• A. $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
• B. $V=\frac{1}{2\pi {\epsilon }_0}\frac{q}{r}$
• C. $V=\frac{1}{\pi {\epsilon }_0}\frac{q}{r}$
• D. $V=\frac{3}{4\pi {\epsilon }_0}\frac{q}{r}$

Answer 1

The correct option is A $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$

A negatively charge -q will be induced on the inner surface of cavity and positive charge +q will be induced on the outer surface, which will be uniformly distributed. There will be no field or potential at point P due to inner charges +q and -q. Potential at P will only be due to outer +q charge. So
$V_P=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$