Question

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

• A. $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)$
• B. $2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}$
• C. $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2}$
• D. $\frac{1}{\sqrt{3}} \frac{\tau}{ Bi }$

Answer 1

Answer: (B)

The current flowing clockwise in an equilateral triangle has a magnetic field in the direction of $\hat{k}$.
$\tau=B I N A \sin \theta$
$\tau=B I N A \sin 90^{\circ}$
Area of equilateral triangle $A=\frac{\sqrt{3}}{4}I^{2}, N=1$
$\tau=B I\left(\frac{\sqrt{3}}{4}I^{2}\right)$
$I^{2}=\left(\frac{4 \tau}{\sqrt{3} B I}\right)$
$I=\left(\frac{4 \tau}{\sqrt{3} B I}\right)^{\frac{1}{2}}$