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An equilateral triangular coil of side l is placed between the pole pieces of a permanent magnet so that the magnetic field B lies in the plane of the coil. If a current i flowing through the triangle produces a torque τ on it, then the side length l of the triangle is

1. (2/√3)(τ/Bl)
2. 2(τ/√3Bl)^(1/2)
3. (2/√3)(τ/Bl)^(1/2)
4. (1/√3)(τ/Bl)

Correct answer: 2(τ/√3Bl)^(1/2)

Solution

With B in the coil's plane, torque tau = i*A*B = i*(sqrt3/4)*l^2*B. Solving, l = 2*sqrt(tau/(sqrt3 * B * i)), which is index 1.

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