Question

A rectangular coil (Dimension \(5\ \mathrm{cm} \times 2.5\ \mathrm{cm}\)) 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 \(45^\circ\) about Z-axis, then the torque on the coil is :

• A. \(0.42\) Nm
• B. \(0.55\) Nm
• C. \(0.38\) Nm
• D. \(0.27\) Nm

Hint:

Torque is \(NIAB\sin\theta\), where \(\theta\) is the angle between the coil normal and \(\vec{B}\). The coil normal starts along Y and is rotated by \(45^\circ\) about Z.

Answer 1

The Correct Option is D

Area \(A = 0.05 \times 0.025 = 1.25 \times 10^{-3}\ \mathrm{m^2}\). Magnetic moment \(M = NIA = 100 \times 3 \times 1.25 \times 10^{-3} = 0.375\ \mathrm{A\,m^2}\).
The coil is in the X-Z plane, so its normal is along Y, perpendicular to \(\vec{B}\) (along X). Tilting by \(45^\circ\) about the Z-axis turns the normal in the X-Y plane, making \(45^\circ\) with \(\vec{B}\) (or \(135^\circ\), same sine).
\(\tau = MB\sin 45^\circ = 0.375 \times 1 \times 0.707 = 0.265 \approx 0.27\) Nm.
Answer: (4) \(0.27\) Nm