PYQ NEET- Moving Charges And Magnetism L-9

Question: A closely wound solenoid of 2000 turns and area of cross-section $1.5 \times 10^{-4} \mathrm{~m}^2$ carries a current of $2.0 \mathrm{~A}$. 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 $30^{\circ}$ with the axis of the solenoid. The torque on the solenoid will be#

A) $3 \times 10^{-3} \mathrm{~N} \mathrm{~m}$

B) $1.5 \times 10^{-3} \mathrm{~N} \mathrm{~m}$

C) $1.5 \times 10^{-2} \mathrm{~N} \mathrm{~m}$

D) $3 \times 10^{-2} \mathrm{~N} \mathrm{~m}$

Answer: (C) $1.5 \times 10^{-2} \mathrm{~N} \mathrm{~m}$#

Sol:#

Magnetic moment of the loop. $$ M=N I A=2000 \times 2 \times 1.5 \times 10^{-4}=0.6 \mathrm{~J} / T $$

Torque $\tau=\mathrm{MBsin} 30^{\circ}$ $$ =0.6 \times 5 \times 10^{-2} \times \frac{1}{2}=1.5 \times 10^{-2} \mathrm{Nm} $$