Question

A point charge $Q$ lies on the perpendicular bisector of an electric dipole of dipole $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole).then the electric field at $\theta$ is proportional to :

• A. $P^2$ and $r^{-3}$
• B. $P$ and $r^{-2}$
• C. $P^{-1}$ and $r^{-2}$
• D. $P$ and $r^{-3}$

Answer 1

The correct option is D $P$ and $r^{-3}$

$\begin{array}{c}Aswehave,\\ ifr>1\\ P_{axi}=\frac{1}{4\pi E_0}\frac{2P}{r^3}\\ V_{axi}=\frac{1}{4\pi E_0}\frac{P}{r^2}\\ Wherein,\\ Anglebetween{P}_{axi}andPis0.\\ E_{equatorial}=\frac{kp}{r^3}\\ i.eE\propto p\\ andP\propto r^{-3}\end{array}$

Hence, Option $D$ is correct answer.