Module 3 : MAGNETIC FIELD
Lecture 14 : Torque on a Current Loop in a Uniform Magnetic Field

\includegraphics{fig3.14.eps}

The net force on the loop is zero because of equal and opposite forces acting on diametrically opposite elements of the loop. However, the torques due to all the elements are parallel to the y-direction and add up. The net torque is obtained by integrating over all the elements

\begin{displaymath}\vec\tau = IR^2B\int_0^{2\pi}\sin^2\theta d\theta \hat\jmath = IR^2B\pi\hat\jmath = IBA\hat\jmath\end{displaymath}

where $A=\pi R^2$is the area of the loop.

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