Q. Two equal charges $q$ of opposite sign separated by a distance $2a$ constitute an electric dipole of dipole moment $p.$ If $P$ is a point at a distance $r$ from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole, then the potential at $P$ is given by $(r > > 2a)(Where\ p = 2\ qa)$
A) $V = \frac{p\cos\theta}{4\pi\varepsilon_{0}r^{2}}$
B) $V = \frac{p\cos\theta}{4\pi\varepsilon_{0}r}$
C) $V = \frac{p\sin\theta}{4\pi\varepsilon_{0}r}$
D) $V = \frac{p\cos\theta}{2\pi\varepsilon_{0}r^{2}}$
Explanation
(a) For the given situation, diagram can be drawn as follows
As shown in figure component of dipole moment along the line $OP$ will be $p^{'} = p\cos\theta$
Hence electric potential at point $P$ will be
$V = \frac{1}{4\pi\varepsilon_{0}}.\frac{p\cos\theta}{r^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.