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. $\frac{2}{\sqrt{3}}\left(\frac{\tau }{Bi}\right)$
• B. $2{\left(\frac{\tau }{\sqrt{3}Bi}\right)}^{1/2}$
• C. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{Bi}\right)}^{1/2}$
• 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 $\hat{k}$.
$\tau =BINA\sin \theta$
$\tau =BINA\sin 90^{\circ }$
Area of equilateral triangle $A=\frac{\sqrt{3}}{4}{I}^2,N=1$
$\tau =BI\left(\frac{\sqrt{3}}{4}{I}^2\right)$
$I^2=\left(\frac{4\tau }{\sqrt{3}BI}\right)$
$I={\left(\frac{4\tau }{\sqrt{3}BI}\right)}^{\frac{1}{2}}$