Question

A short magnet produces a deflection of ${45}^o$ when placed at some distance in $\tan A$ position of the deflection magnetometer. If another magnet of same length and pole strength is kept at the same distance in $\tan B$ position then the deflection produced is :

• A. ${\tan }^{-1}\left(\frac{1}{2}\right)$
• B. ${\tan }^{-1}\left(2\right)$
• C. ${\tan }^{-1}\left(0.25\right)$
• D. ${\tan }^{-1}\left(0.75\right)$

Answer 1

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

Magnteic field of a magnet in $\tan A$ position is:

$\frac{{\mu }_o}{4\pi }\frac{2M_A}{d^3}=B_H\tan {\theta }_A$
Magnetic field of a magnet in $\tan B$ position is:

$\frac{{\mu }_o}{4\pi }\frac{M_B}{d^3}=B_H\tan {\theta }_B$
$\frac{\tan {\theta }_A}{\tan {\theta }_B}=2$

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

${\theta }_B={\tan }^{-1}\left(0.5\right)$