Question

An electric dipole is placed at the origin and is directed along the x-axis. At a point P, far away from the dipole,the electric field is parallel to the y-axis. OP makes an angle $\theta$ with the x-axis. Then,

• A. $\tan \theta =\sqrt{3}$
• B. $\tan \theta =\sqrt{2}$
• C. $\tan \theta =1$
• D. $\tan \theta =\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

$\tan \theta =\sqrt{2}$

As we Know

$\tan \alpha =\frac{1}{2}\tan \theta$

because

$E\cos \alpha =\frac{2\beta \cos \theta }{4\pi {\in }_0{r}^3}$

$Esin\alpha =\frac{\beta sin\theta }{4\pi {\in }_0{r}^3}$

$or\tan \alpha =\frac{1}{2}\tan \theta$

$\theta +\alpha ={90}^{\circ }or\theta ={90}^{\circ }-\alpha$

$\tan \theta =\cot \alpha =\frac{1}{\tan \alpha }=\frac{2}{\tan \theta }$

$or\tan \theta =\sqrt{2}$