A coil, in the shape of an equilateral triangle of side l , is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I

Question

A coil, in the shape of an equilateral triangle of side l , is suspended between two pole pieces of a permanent magnet, such that the magnetic field B is in the plane of the coil. If due to current I in the triangle, a torque τ acts on it, the side l of the triangle is

TestHub · Accepted Answer

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

$τ = I A B s i n θ$

Area of $Δ L M N : A = \frac{\sqrt{3}}{4} l^{2}$

and $θ = 90^{o}$

Substituting the given values in the expression for torque, we have

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

$∴ l = 2 {(\frac{τ}{\sqrt{3} B I})}^{\frac{1}{2}}$

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