The magnetic potential energy of a bar magnet of magnetic moment $\vec{m}$ placed in a uniform magne

Question

The magnetic potential energy of a bar magnet of magnetic moment $\vec{m}$ placed in a uniform magnetic field $\vec{B}$ is completely maximized when the angle between them is $180^{\circ}$. What is the value of this potential energy, if we follow the usual convention?

Professor PC Thomas Classes · Answer

(a) : The magnetic potential energy of a magnetic dipole in a uniform magnetic field is given by $U = -\vec{m} \cdot \vec{B} = -mB \cos	heta$. When the dipole is aligned anti-parallel to the field ($	heta = 180^{\circ}$), it is in unstable equilibrium and possesses maximum potential energy. Substituting $	heta = 180^{\circ}$, we get $U = -mB \cos(180^{\circ}) = -mB (-1) = +mB$.