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A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B⃗ is in the plane of the coil. If due to a current i in the triangle a torque τ acts on it, the side l of the triangle is:
- 2/√3 (τ/Bi) 1/2
- (τ/√3Bi) 1/2
- 2/√3 (τ/Bi)
- 1/√3 τ/Bi
Correct answer: (τ/√3Bi) 1/2
Solution
The torque on a current-carrying loop in a magnetic field is given by τ = n * i * A * B, where A is the area of the loop. For an equilateral triangle, A = (√3/4) * l². Solving for l, we get l = (τ / (√3 * B * i))^(1/2).
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