A coil in the shape of an equilateral triangle 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 τ rests on it, the

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Correct answer: A. 2 ( τ 3 Bi )(1)/(2)

Torque acting on equilateral triangle in a magnetic field $B$ is

$τ = iABsin\theta$

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet

Area of triangle $LMN$ ,

$A = \dfrac{3}{2}l^{2} and$ \theta = 90 ° $Substituting the given values in expression for torque, we get$ τ = i \times \dfrac{3}{4}l^{2}Bsin90 ° $$ τ = \dfrac{3}{4}il^{2}B $~ \left(∵ \sin 90 ° = 1\right)$

$l^{2} = \dfrac{4τ}{\sqrt{3}Bi}$

Here, $l = 2\left(\dfrac{τ}{\sqrt{3}Bi}\right)\dfrac{1}{2}$

A coil in the shape of an equilateral triangle of side l is...

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