Question

Two short magnets with their axes horizontal and perpendicular to the magnetic meridian are placed with their centres $40\text{cm}$ east and $50\text{cm}$ west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments $M_1:M_2$ is

• A. $2:\sqrt{5}$
• B. $64:125$
• C. $16:25$
• D. $4:5$

Answer 1

The correct option is B $64:125$


From the diagram, $B_{a{x}_1}=B_{a{x}_2}$

Thus, $\frac{{\mu }_0}{4\pi }\frac{2M_1}{d_1^3}=\frac{{\mu }_0}{4\pi }\frac{2M_2}{d_2^3}$

$\therefore \frac{M_1}{M_2}={\left(\frac{d_1}{d_2}\right)}^3={\left(\frac{40}{50}\right)}^3=\frac{4^3}{5^3}$

$M_1:M_2=64:125$

Hence, option (b) is the correct answer.