The potential energy u of a magnetic dipole latex: \vec{\mu} in an external magnetic field latex: \vec{b} can be found by finding (integrating) the work done by the torque latex: \left|\vec{\tau}\right|=\left|\vec{ \mu}\times\vec{b}\right|=\mu b \sin\theta on the dipole as the dipole rotates through an angle latex: \theta in other words latex: u=-w=-\int\vec{\tau}\cdot d\vec{\theta}=\int \mu b \sin\theta d\theta this gives latex: u=-\vec{\mu}\cdot\vec{b}=-\mu b \cos\theta , where latex: \theta is the angle between the magnetic dipole moment and the external magnetic field. how much more potential energy, then, does a dipole have if it points opposite to an external magnetic field (highest energy state) than it does when it points in the same direction (lowest energy state) as the magnetic field?

μb

2μb

0

0.5μb