Force on a Current-Carrying Conductor

$F = B I l \sin\theta \qquad \vec{F} = I\,\vec{l} \times \vec{B}$

The direction follows Fleming's left-hand rule (motors): First finger = Field, seCond finger = Current, thuMb = Motion. Fleming's right-hand rule gives the direction of induced current in generators.

A coil of $N$ turns and area $A$ in a field experiences torque $T = NBIA\cos\alpha$ — the basis of DC motors and moving-coil meters.