Question

An electric dipole is placed along the x-axis at the origin 0. A point P is at a distance of 20 cm from this origin such that OP makes an angle $\text{/3}$ with the x-axis. If the electric field at P makes an angle $\theta$ with the x-axis, the value of $\theta$ would be

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{3}+{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
• C. $\frac{2\pi }{3}$
• D. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Answer 1

Answer: (B)

Component of electric field at point P parallel to $X-$ axis,
$E_X=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{2(p\cos \pi /3)}{r^3}$ $\frac{1}{4\pi {\epsilon }_0}\cdot \frac{P}{r^3}$ Component of electric field of point $P$ perpendicular to $X-$ axis, $E_Y=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{p\sin \pi /3}{r^3}$ $=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\sqrt{3}p}{2r^3}$ $\therefore$ $\tan \theta =\frac{E_Y}{E_X}=\frac{\sqrt{3}}{2}$ $\therefore$ $\theta ={\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$