Question

A coil in the shape of an equilateral triangles of side l is suspended between the pole pieces of a permanent magnet such that 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. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{Bi}\right)}^{1/2}$
• B. $\frac{2}{3}\left(\frac{\tau }{Bi}\right)$
• C. $2{\left(\frac{\tau }{\sqrt{3}Bi}\right)}^{1/2}$
• D. $\frac{1}{\sqrt{3}}\frac{\tau }{Bi}$

Answer 1

The correct option is C $2{\left(\frac{\tau }{\sqrt{3}Bi}\right)}^{1/2}$

Torque acting an equilateral triangle in magnetic field B is

$\tau =iAB\sin \theta$ ...(i)

Area of triangle LMN

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

and $\theta ={90}^o$

$\tau =i\times \frac{\sqrt{3}}{4}{l}^2$

$=\frac{\sqrt{3}}{4}i{l}^{2}B(\therefore \sin {90}^o=1)$

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