Question

The ratio of magnetic moments of two bar magnets is $4:5$. If the deflection due to first bar magnet in deflection magnetometer is ${45}^o$, then the deflection due to the second bar magnet is :
(in equal distance method)

• A. ${\tan }^{-1}\left(1.25\right)$
• B. ${\tan }^{-1}\left(0.25\right)$
• C. ${\tan }^{-1}\left(1\right)$
• D. ${\tan }^{-1}\left(0.75\right)$

Answer 1

The correct option is A ${\tan }^{-1}\left(1.25\right)$

The deflection off the magnetic needle in tan A position by a short magnet is given by
$\frac{{\mu }_o}{4\pi }\frac{2M_A}{d^3}=B_H\tan {\theta }_A$
$\frac{\tan {\theta }_A}{\tan {\theta }_B}=\frac{M_A}{M_B}$
$\tan {\theta }_B=\frac{5}{4}$
${\theta }_B={\tan }^{-1}\left(1.25\right)$