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

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 B is in plane of the coil. If due to a current i in the triangle, a torque τ rests on it, the side l of the triangle is

TestHub · Accepted Answer

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

$τ = i A B \sin θ$

Area of triangle $LMN$ ,

$A = \frac{\sqrt{3}}{2} l^{2}$ and $θ = 90 °$

Substituting the given values in expression for torque, we get

$τ = i \times \frac{\sqrt{3}}{4} l^{2} B \sin 90 °$

$τ = \frac{\sqrt{3}}{4} i l^{2} B$ $(∵ \sin 90 ° = 1)$

$l^{2} = \frac{4 τ}{\sqrt{3} B i}$

Here, $l = 2 {(\frac{τ}{\sqrt{3} B i})}^{\frac{1}{2}}$

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