Physics

A current loop in a magnetic field experiences a torque that tries to align its magnetic moment with the field. The key insight is that work equals the change in rotational potential energy: as you rotate the loop against this torque, you're fighting the field's tendency to keep the loop aligned. Since the magnetic potential energy is $U = -\mu B \cos\theta$ (where $\mu = IA$ is the magnetic moment), rotating $180°$ flips the loop from its lowest energy state to its highest, and the work you must supply equals that total energy change.

A current loop in a magnetic field experiences a torque that tries to align its magnetic moment with the field. The key insight is that work equals the change in rotational potential energy: as you rotate the loop against this torque, you're fighting the field's tendency to keep the loop aligned. Since the magnetic potential energy is $U = -\mu B \cos\theta$ (where $\mu = IA$ is the magnetic moment), rotating $180°$ flips the loop from its lowest energy state to its highest, and the work you must supply equals that total energy change.