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A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clockwise 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, the torque on the coil is:

1. 0.38 Nm
2. 0.55 Nm
3. 0.42 Nm
4. 0.27 Nm

Correct answer: 0.27 Nm

Solution

m = N*i*A = 100*3*(0.05*0.025) = 0.375 A m^2. With coil in X-Z plane its normal is along Y (perpendicular to B along X). Tilting 45 deg about Z makes the angle between m and B equal 45 deg, so tau = m*B*sin45 = 0.375*1*0.707 = 0.27 Nm.

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