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A rectangular coil (dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is -

1. 0.55 N m
2. 0.38 N m
3. 0.42 N m
4. 0.27 N m

Correct answer: 0.27 N m

Solution

The torque on a coil in a magnetic field is calculated using the formula τ = n * I * A * B * sin(θ), where n is the number of turns, I is the current, A is the area of the coil, B is the magnetic field strength, and θ is the angle between the magnetic field and the normal to the coil's plane. In this case, the area of the coil is 0.0125 m², the angle after tilting is 45°, and substituting these values gives the correct torque of 0.27 N m.

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