Physics - Magnetism Question with Solution | TestHub

The torque on a magnetic dipole in a uniform magnetic field is $\vec{\tau }=\vec{M}\times \vec{B}$, with magnitude $\tau =MB\sin \theta$. Torque is maximum when $\theta =90^{\circ }$ (perpendicular), not parallel. So A is incorrect. The potential energy is $U=-\vec{M}\cdot \vec{B}=-MB\cos \theta$. Potential energy is minimum (stable equilibrium) when $\theta =0^{\circ }$ (parallel), not anti-parallel. So B is incorrect. In a uniform magnetic field, the net force on a magnetic dipole is always zero. So C is correct. The stable equilibrium position is when ${\theta }_i=0^{\circ }$, so $U_i=-MB\cos 0^{\circ }=-MB$. Rotating it by $90^{\circ }$ means ${\theta }_f=90^{\circ }$, so $U_f=-MB\cos 90^{\circ }=0$. The work done by the external agent is $W_{ext}=\Delta U=U_f-U_i=0-(-MB)=MB$. So D is correct.