Question

An electric dipole of moment $\overrightarrow{p}$ is placed at the origin along the x-axis. The angle made by electric field with x-axis at a point P, whose position vector makes an angle $\theta$ with x-axis, is ( where $\tan \alpha =\frac{1}{2}\tan \theta$)

• A. $\alpha$
• B. $\theta$
• C. $\theta +\alpha$
• D. $\theta +2\alpha$

Answer 1

The correct option is C $\theta +\alpha$

An electric dipole of moment $=\overline{p}$

electric field $x-$axis at a point $=p$

angle $=\theta$ with $x-$axis

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

$(\theta +\alpha )=$ the value of the position vector makes an angle $\theta$

$\theta ={60}^0+\alpha$

now resolving $E$ into its components

$E\cos \alpha =\frac{2p\cos {60}^0}{4\pi {ϵ}_0{r}^3}⟶\left(1\right)$

$E\sin \alpha =\frac{p{\sin 60}^0}{4\pi {ϵ}_0{r}^3}⟶\left(2\right)$

Dividing $2$ by $1$

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

$\tan \alpha =\tan (\theta +\alpha )$

$\alpha =\theta +\alpha$