Question

An electric dipole is placed along the x-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle $\frac{\pi}{3}$ with the x-axis. If the electric field at P makes an angle θ with x-axis, the value of θ 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)

$\frac{\pi}{3} + \tan^{- 1}\left( \frac{\sqrt{3}}{2} \right)$

Answer 2

According to question we can draw following figure.

As we have discussed earlier in theory $\theta = \frac{\pi}{3} + \alpha$

$\tan\alpha = \frac{1}{2}\tan\frac{\pi}{3}$⇒ $\alpha = \tan^{- 1}\frac{\sqrt{3}}{2}$

So, $\theta = \frac{\pi}{3} + \tan^{- 1}\frac{\sqrt{3}}{2}$