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 magnetic field of intensity $B$ is along the plane of the coil. If due to a current $I$ in the triangle, a torque $\tau$ acts on it, then side $l$ of the triangle is :

• A. $\frac{1}{\sqrt{3}}\left(\frac{\tau }{BI}\right)$
• B. $2{\left(\frac{\tau }{\sqrt{3}BI}\right)}^{\frac{1}{2}}$
• C. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{BI}\right)}^{\frac{1}{2}}$
• D. $4{\left(\frac{\tau }{\sqrt{3}BI}\right)}^{\frac{1}{2}}$

Answer 1

The correct option is B $2{\left(\frac{\tau }{\sqrt{3}BI}\right)}^{\frac{1}{2}}$

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 $A=\frac{\sqrt{3}}{4}{l}^2,N=1$

$\tau =BI\left(\frac{\sqrt{3}}{4}{l}^2\right)$
$l^2=\left(\frac{4\tau }{\sqrt{3}BI}\right)$
$l={\left(\frac{4\tau }{\sqrt{3}BI}\right)}^{\frac{1}{2}}$