Question

A magnet of magnetic moment $M$ is lying in a magnetic field of induction $B . W_{1}$ is the work done in turning it from $0^{\circ}$ to $60^{\circ}$ and $W_{2}$ is the work done in turning it from $30^{\circ}$ to $90^{\circ}$. Then

• A. $W_{2}=\frac{W_{1}}{2}$
• B. $W_{2}=2 W_{1}$
• C. $W_{2}=W_{1}$
• D. $W_{2}=\sqrt{3} W_{1}$

Answer 1

Answer: (D)

As $W=-M B\left(\cos \theta_{2}-\cos \theta_{1}\right)$
$W_{1}=-M B\left[\cos 60^{\circ}-\cos 0^{\circ}\right]=-M B\left(\frac{1}{2}-1\right)=\frac{M B}{2}$
$W_{2}=-M B\left(\cos 90^{\circ}-\cos 30^{\circ}\right)=-M B\left(0-\frac{\sqrt{3}}{2}\right)=\frac{\sqrt{3} M B}{2}$
$W_{2}=\sqrt{3} W_{1}$