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 $\tau = MB \sin \theta$
$\tau_1 =MB_1 \sin 90^\circ=MB_1$
$\tau_2 = MB_2 \sin 90^\circ = MB_2 $
or $ \frac{MB_1}{MB_2}=\frac{\tau_1}{\tau_2}$
$\therefore \frac{B_1}{B_2}=\frac{\tau_1}{\tau_2}$