Question

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

• 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 $\overset{ \rightarrow }{p}=\hat{i}+\sqrt{3}\hat{j}=\overset{ \rightarrow }{p_{1}}+\overset{ \rightarrow }{p_{2}}$
Therefore $\overset{ \rightarrow }{p_{1}}=\hat{i}$ and $\overset{ \rightarrow }{p_{2}}=\sqrt{3}\hat{j}$

Field due to $\overset{ \rightarrow }{p_{1}}$ at point $B$ ,
$E_{1}=\frac{2 \times K}{2^{3}}=\frac{K}{4}$
Field due to $\overset{ \rightarrow }{p_{2}}$ at point $B$ ,
$E_{2}=\frac{K \times \sqrt{3}}{8}$
$E_{n e t}=\sqrt{E_{1}^{2} + E_{2}^{2}}$
$E_{n e t}=\sqrt{\frac{K^{2}}{16} + \frac{K^{2} \times 3}{64}}$
$E_{n e t}=\frac{\sqrt{7} K}{8}$