Question

Torques $ \tau _{1}\,$ and $\tau_{2}$ are required for magnetic needle to remain perpendicular to the magnetic fields $B_1$ and $B_2$ at two different places. The ratio $B_1/B_2$ is

• A. $ \frac{\tau _{2}}{\tau _{1}} $
• B. $ \frac{\tau _{1}}{\tau_{2}} $
• C. $ \frac{\tau _{1}+\tau _{2}}{\tau _{1}-\tau _{2}} $
• D. $ \frac{\tau _{1}-\tau _{2}}{\tau _{1}+\tau _{2}} $

Answer 1

Answer: (B)

$ Torque, \tau =M B \sin \theta $
$ \tau_{1} =M B_{1} \sin 90^{\circ}=M B_{1} $
$ \tau_{2} =M B_{2} \sin 90^{\circ}=M B_{2} $
or $ \frac{M B_{1}}{M B_{2}} =\frac{\tau_{1}}{\tau_{2}} $
$\therefore \frac{B_{1}}{B_{2}} =\frac{\tau_{1}}{\tau_{2}}$