Question

A dipole having dipole moment $p$ is in front of a solid uncharged conducting sphere as shown in the figure. The net potential at point A lying on the surface of the sphere is: (where, $K=\frac{1}{4\pi {\epsilon }_0}$)

• A. $\frac{Kpcos\varphi }{r^2}$
• B. $\frac{Kpco{s}^2\varphi }{r^2}$
• C. zero
• D. $\frac{2Kpco{s}^2\varphi }{r^2}$

Answer 1

The correct option is B $\frac{Kpco{s}^2\varphi }{r^2}$

Electric potential due to an electric dipole:
$V=\frac{K\overrightarrow{p}.\overrightarrow{r}}{r^3}$

Potential at the centre of sphere
$V=\frac{K\overrightarrow{p}\left(\frac{r}{\cos \varphi }\right)}{(\frac{r}{\cos \varphi }{)}^3}=\frac{Kp{\cos }^2\varphi }{r^2}$

$\because$ This is conducting sphere, so potential at all points of sphere is same.