Question

A short dipole is placed along $x-$ axis with centre at origin ($\text{O}$). The electric field at a point $\text{P}$ due to dipole such that $\overrightarrow{\text{OP}}$ makes an angle of ${45}^{\circ }$ with the $x-$ axis, is directed along a direction making

• A. ${\tan }^{-1}\left(0.5\right)$ with $x-$ axis
• B. $\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$ with $x-$ axis
• C. $\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$ with $y-$ axis
• D. ${\tan }^{-1}\left(0.5\right)$ with $y-$ axis

Answer 1

The correct option is B $\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$ with $x-$ axis


Given, $\theta ={45}^{\circ }$

Let $\alpha$ be the angle making by net electric field at point $\text{P}$ with $\text{OP}$.

So, from the formula,

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

$\Rightarrow \tan \alpha =\frac{\tan {45}^{\circ }}{2}\Rightarrow \tan \alpha =0.5$

$\Rightarrow \alpha ={\tan }^{-1}\left(0.5\right)$

Thus, the angle which $E_{net}$ makes with $x-$ axis is ${45}^{\circ }+{\tan }^{-1}\left(0.5\right)=\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$

So, $\left(b\right)$ is correct option.