Torque on a Current Carrying Coil placed in a Uniform Magnetic Field —
When a current carrying coil is placed in a uniform magnetic field, the net force on it is always zero but different parts of the coil experience forces in different directions. Due to it, the coil may experience a torque or couple.
When a coil of area $A$ having $N$ turns, carrying current $I$ is placed in uniform magnetic field $B$, it will experience torque which is given by
$\tau=N I A B \sin \theta=M B \sin \theta$
where $M=N I A$ and $\theta$ is the angle between the direction of magnetic field and normal to the plane of the coil.
Special Cases :
- If the plane of the coil is perpendicular to the direction of magnetic field i.e. $\theta=0^{\circ}$, then $\tau=0$ (minimum)
- If the plane of the coil is parallel to the direction of magnetic field i.e. $\theta=90^{\circ}$, then
$\tau=N i A B$ (maximum)
If $\alpha$ is the angle between plane of the coil and the magnetic field, then torque on the coil is
$\tau=N I A B \cos \alpha=M B \cos \alpha$
