A rectangular coil of length 0.12 m and width 0.1 m having

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A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 weber/m². The coil carries a current of 2A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be :

1. 0.20 Nm
2. 0.24 Nm
3. 0.12 Nm
4. 0.15 Nm

Correct Option: A

Here, number of turns of coil, N = 50
Current through the coil I = 2A
Area A = l × b = 0.12 × 0.1m²
Magnetic field ^→_B = 0.2 ω/m²

Torque required to keep the coil in stable equilibrium.
τ = ^→_M × ^→_B sin 60° = Ni AB sin 60°
= 50 × 2 × 0.12 × 0.1 × 0.2 × √3/2
= 12√3 × 10^{-2 = 0.20784 Nm}