Physics - Magnetism Question with Solution | TestHub

The potential energy of a magnetic dipole in a uniform magnetic field is given by $U=-\vec{M}\cdot \vec{B}=-MB\cos \theta$, where $\theta$ is the angle between the magnetic moment $\vec{M}$ and the magnetic field $\vec{B}$.

Initially, the magnetic moment is parallel to the field, so ${\theta }_1=0^{\circ }$. The initial potential energy is $U_1=-MB\cos (0^{\circ })=-MB$.

Finally, the magnetic moment is perpendicular to the field, so ${\theta }_2=90^{\circ }$. The final potential energy is $U_2=-MB\cos (90^{\circ })=0$. The work done in rotating the magnet is $W=U_2-U_1=0-(-MB)=MB$. Given $M=1.5$ A m${}^2$ and $B=0.4$ T. So, $W=1.5\times 0.4=0.6$ J. We need to find $N$ such that $W=N\times 10^{-1}$ J. So, $0.6=N\times 0.1$, which gives $N=6$.