Question

The magnitude of electric field intensity at point $B$ $(2,0,0)$ due to a dipole of dipole moment $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin is (assume that the point $B$ is at a large distance from the dipole and $K=\frac{1}{4\pi {ϵ}_0}$ )

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

Answer 1

Answer: (C)

Let $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}=\overrightarrow{p_1}+\overrightarrow{p_2}$
Therefore $\overrightarrow{p_1}=\hat{i}$ and $\overrightarrow{p_2}=\sqrt{3}\hat{j}$

Field due to $\overrightarrow{p_1}$ at point $B$ ,
$E_1=\frac{2\times K}{2^3}=\frac{K}{4}$
Field due to $\overrightarrow{p_2}$ at point $B$ ,
$E_2=\frac{K\times \sqrt{3}}{8}$
$E_{net}=\sqrt{E_1^2+E_2^2}$
$E_{net}=\sqrt{\frac{K^2}{16}+\frac{K^2\times 3}{64}}$
$E_{net}=\frac{\sqrt{7}K}{8}$