A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying… | JEE Main 2019 (9 Apr, Shift 1)

Q72JEE Main 2019 · 9 APR · SHIFT 1Medium

Current Loop as a Magnetic Dipole

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:

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Answer: (d)

$m = NIA = 100 \times 3 \times (0.05 \times 0.025) = 0.375\text{ A m}^2$
Coil in the X-Z plane has $\vec m$ along $Y$ , i.e. $90^\circ$ to $\vec B$ ; after tilting $45^\circ$ about $Z$ the angle is $45^\circ$ .
$\tau = mB\sin45^\circ = 0.375 \times 1 \times 0.707 \approx 0.27\text{ N m}$
So the answer is (d) 0.27 N m.

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