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The net force on a current loop in a uniform magnetic field is zero, yet there exists a torque that forces the loop to rotate. The net torque acting on a conducting loop is:
$$ \vec{\tau}=\vec{\mu} \times \vec{B} $$ where $$ \vec\mu=I\vec A $$ is called magnetic dipole moment or magnetic moment. More generally, one can show that $$ \vec{\mu}=\frac{1}{2} I \oint_{C} \mathbf{r} \times d \mathbf{l} $$ We can associate a magnetic energy as $$ U=-\vec{\mu} \cdot \vec{B}=-\mu B \cos \phi $$Remarks
- The right-hand rule determines the direction of the magnetic moment of a current-carrying loop.
- This result is analogous to the torque exerted by an electric field on an electric dipole.
Lenz's Law