Question

A coil, in the shape of an equilateral triangle of side $l$ , is suspended between two pole pieces of a permanent magnet, such that the magnetic field $B$ is in the plane of the coil. If due to current $I$ in the triangle, a torque $\tau$ acts on it, the side $l$ of the triangle is

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

Answer 1

Answer: (A)

Torque acting on an equilateral triangle in a magnetic field $B$ is
$\tau=IAB \, sin\theta $
Area of $\Delta LMN:A=\frac{\sqrt{3}}{4}l^{2}$
and $\theta =90^{o}$
Substituting the given values in the expression for torque, we have

$\tau=I\times \frac{\sqrt{3}}{4}l^{2} \, Bsin90^\circ =\frac{\sqrt{3}}{4}I \, l^{2}B$
$\therefore l=2\left(\frac{\tau}{\sqrt{3} B I}\right)^{\frac{1}{2}}$