Question

The electric field at a point due to an electric dipole, or an axis inclined at an angle $\theta (<{90}^o)$ to the dipole axis, is perpendicular to the dipole axis, if the angle $\theta$ is

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

Answer 1

The correct option is C ${\tan }^{-1}\left(\sqrt{2}\right)$

So, here, when we take an axis inclined at angle $\theta$ to dipole axis,

and if the net field from that inclined axis makes angle $\theta$, then,

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

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

So, from figure,clearly,

$\alpha +\theta =90$

therefore, $\theta =90-\alpha$

So, $tan\theta =tan(90-\alpha )$

$tan\theta =cot\alpha$...... (using trigonometric relation).............(2)

From eqns.(1) and (2),

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

$ta{n}^2\theta =2$

$tan\theta =\sqrt{2}$

$\theta =ta{n}^{-1}\sqrt{2}$