A coil in the shape of an equilateral triangle of side $l$ is suspended between the pole pieces of a permanent magnet such that $\vec {B}$ is in plane of the coil. If due to a current $i$ in the triangle a torque $\tau$ acts on it, the side $l$ of the triangle is
AIPMT 2005, Medium
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The current flowing clockwise in an equilateral triangle has a magnetic field in the direction of $\hat{ k }$
$\tau=\operatorname{BiN} A \sin \theta$
$\tau=\operatorname{BiN} A \sin 90^{\circ}$
$\tau= Bi \times \frac{\sqrt{3}}{4} I ^{2} \times 1$
$\left[\because\right.$ Area of equilateral triangle $=\frac{\sqrt{3}}{4} I ^{2}$ and $\left. N =1\right]$
$\Rightarrow I ^{2}=\frac{4 \tau}{\sqrt{3} Bi } \Rightarrow I =2\left[\frac{\tau}{ Bi \sqrt{3}}\right]^{1 / 2}$
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