Question

When a D.M. is set in $\tan A$ position, the deflection is ${30}^o$ for a magnet A placed at a distance of $40cm$ from the midpoint of the D.M. When the D.M. is kept in $\tan B$ position another magnet B produces a deflection of ${60}^o$, when placed at the same distance. The ratio of the magnetic moments of A and B is :

• A. $1:2$
• B. $1:3$
• C. $2:3$
• D. $1:6$

Answer 1

The correct option is D $1:6$

The deflection off the magnetic needle in tan A position by a short magnet is given by
$\frac{{\mu }_o}{4\pi }\frac{2M_A}{d^3}=B_H\tan {\theta }_A$
The deflection off the magnetic needle in tan B position by a short magnet is given by
$\frac{{\mu }_o}{4\pi }\frac{M_B}{d^3}=B_H\tan {\theta }_B$
$\frac{\tan {\theta }_A}{\tan {\theta }_B}=\frac{2M_A}{M_B}$
$\frac{M_A}{M_B}=\frac{1}{2}\times \frac{\tan 30}{\tan 60}=\frac{1}{6}$