Question

The ratio of the magnetic moment of two short magnets when they give zero deflection in $\tan B$ position when placed at $12cm$ and $18cm$ from centre of a deflection magnetometer is :

• A. $\frac{8}{27}$
• B. $\frac{27}{8}$
• C. $\frac{9}{7}$
• D. $\frac{4}{9}$

Answer 1

The correct option is A $\frac{8}{27}$

The deflection of the magnetic needle in $\tan B$ position by a short magnet is given by ,

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

Since the deflection is zero ,

$\frac{M_A}{M_B}=\frac{d_A^3}{d_B^3}$
$\frac{M_A}{M_B}=\frac{8}{27}$