A closely wound solenoid of $2000$ $turns$ and area of cross-section $1.5 \times 10^{-4}\ m^2$ carries a current of $2.0\, A.$ It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5 \times 10^{- 2}$ $tesla$ making an angle of $30^o $ with the axis of the solenoid. The torque on the solenoid will be
AIPMT 2010, Medium
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Magnetic moment of the loop.
$ M=N I A=2000 \times 2 \times 1.5 \times 10^{-4}=0.6 \,\mathrm{J} / \mathrm{T} $
$\text { Torque } \tau =M B \sin 30^{\circ} $
$=0.6 \times 5 \times 10^{-2} \times \frac{1}{2}=1.5 \times 10^{-2}\, \mathrm{N} \mathrm{m}$
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