Question 224 of 276

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

A$0.42Nm$B$0.55Nm$C$0.38Nm$D$0.27Nm$

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Answer: (D) $0.27Nm$

$Torque=\vec{M}\times \vec{B}$
$=MBsin\theta$
$=\left(niA\right)\left(B\right)sin\theta$
$=100\times 3\times \left(5\times {10}^{-2}\times 2.5\times {10}^{-2}\right)\times 1\times sin{45}^{o}$
$=0.27 Nm$