Question

A bar magnet with magnetic moment M is placed in a space where a magnetic field $B_1$ is acting in ${30}^0$ anticlockwise to S-N direction and another magnetic field $B_2$ is along ${45}^0$ clockwise to S-N direction. The magnitude of $B_1$ is $\sqrt{2}\times {10}^{-2}T$. What should be the magnitude of $B_2$ for the equilibrium of the magnet?

• A. ${10}^{-2}T$
• B. ${10}^{-3}T$
• C. $2\times {10}^{-2}T$
• D. ${10}^{-1}T$

Answer 1

The correct option is A

${10}^{-2}T$

Magnetic field $B_1$ exerts anticlockwise torque ${\tau }_1$ to orient M along itself and magnetic field $B_2$ exerts a clockwise torque ${\tau }_2$ to orient M along itself. For equilibrium,

${\tau }_1={\tau }_2$

$M{B}_{1}sin{\theta }_1=M{B}_{2}sin{\theta }_2$

$\Rightarrow B_2=\frac{B_{1}sin{\theta }_1}{sin{\theta }_2}=\frac{\sqrt{2}\times {10}^{-2}}{\times }sin{30}^{\circ }sin{45}^{\circ }={10}^{-2}T$