Torques $\tau_1$ and $\tau_2$ are required for a magnetic needle to remain perpendicular to the magnetic…
Torques $\tau_1$ and $\tau_2$ are required for a magnetic needle to remain perpendicular to the magnetic fields of $B_1$ and $B_2$ at two different places. The ratio of $B_1: B_2$ is equal to
$\tau_2: \tau_1$
$\tau_1: \tau_2$
$\frac{\tau_1+\tau_2}{\tau_1-\tau_2}$
$\frac{\tau_1-\tau_2}{\tau_1+\tau_2}$
Solution
Given that torques $\tau_1$ and $\tau_2$ are required for a magnetic needle to remain perpendicular to the magnetic field $B_1$ and $B_2$.
We know that, torque acting on a magnet in uniform magnetic field.
$
\therefore \quad \tau=M B \sin \theta
$
where, $\theta=90^{\circ}$ (Given)
Now, $\frac{\tau_1}{\tau_2}=\frac{M B_1 \sin 90^{\circ}}{M B_2 \sin 90^{\circ}}$ Hence, $B_1 / B_2=\tau_1 / \tau_2$