A current-carrying coil in a magnetic field experiences a torque (turning effect). $\vec{\tau }=\vec{m}\times \vec{B}=NI(\vec{A}\times \vec{B})$

• $\tau =NIAB\sin \theta$
• $\theta$ is the angle between the magnetic moment ($NI\vec{A}$) and the magnetic field ($\vec{B}$).
• Alternatively, if $\varphi$ is the angle between the plane of the coil and the field, $\theta =90^{\circ }-\varphi$, so $\tau =NIAB\cos \varphi$.