Module 3 : MAGNETIC FIELD
Lecture 14 : Torque on a Current Loop in a Uniform Magnetic Field
  Example 4 :

A circular loop of radius $R$carrying a current $I$is in the x-y plane. The loop is pivoted about its diameter along the y-axis. A uniform magnetic field $\vec B$acts parallel to the x-axis. Calculate the torque on the loop.

Solution :
Consider a length element $dl = Rd\theta$at an angle $\theta$to the y-axis. The force on the element is $I\vec {dl}\times\vec B$is into the plane of the figure.

The force on the element is

\begin{displaymath}\vec{dF} = -IRB\sin\theta d\theta\hat k\end{displaymath}

The torque due to this force about the y-axis is

\begin{eqnarray*} \vec{d\tau} &=& \vec r\times\vec{dF}\\ &=& (R\sin\theta)\hat\... ...\theta d\theta)\hat k\\ &=& IR^2B\sin^2\theta d\theta\hat\jmath \end{eqnarray*}

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