Q.The potential energy of a magnetic dipole whose dipole moment is $\vec p_m = (-0.5\hat i + 0.4\hat j)$ A m$^2$, kept in a uniform magnetic field $\vec B = 0.2\hat i$ T, is

Rotating a magnetic dipole against its restoring torque, from a reference angle of $90°$ to a general angle $\theta$ with a uniform field $\vec B$, stores potential energy

This is minimum, $U=-p_mB$, when the dipole is aligned with the field ($\theta=0°$) -- the stable equilibrium -- and maximum, $U=+p_mB$, when it is anti-aligned ($\theta=180°$) -- the unstable equilibrium. The work needed to flip a dipole from the st …