Question

The magnitude of electric field intensity at point $\text{P}(2,0,0)$ due to a dipole of dipole moment, $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin is -

$($Assume that the point $\text{P}$ is at large distance from the dipole and $K=\frac{1}{4\pi {ϵ}_0})$

• A. $\frac{\sqrt{7}K}{4}$
• B. $\frac{\sqrt{7}K}{8}$
• C. $\frac{\sqrt{13}K}{4}$
• D. $\frac{\sqrt{15}K}{4}$

Answer 1

The correct option is B $\frac{\sqrt{7}K}{8}$

Given, dipole moment, $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}$

$\therefore \tan \theta =\frac{p_y}{p_x}=\sqrt{3}$

$\Rightarrow \theta ={60}^{\circ }$

The dipole moment makes an angle ${60}^{\circ }$ with $x-$axis and lies in $xy$.

We know that electric field at a point due to a dipole is,

$E=\frac{Kp}{r^3}\sqrt{1+3{\cos }^2\theta }$

$\Rightarrow E=\frac{K\sqrt{1^2+(\sqrt{3}{)}^2}}{2^3}\sqrt{1+3(\cos {60}^{\circ }{)}^2}$

$=\frac{\sqrt{7}K}{8}$