Magnetic Effects & Magnetism

JEE Main level, single correct, medium

256 of 276

Question 256 of 276

A circular coil has moment of inertia 0.8kgm20.8kg{m}^{2} around any diameter and is carrying current to produce a magnetic moment of 20Am220{Am}^{2}. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4T4T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o{60}^{o} will be :

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Answer: (A) 10rads−110rad{s}^{-1}

From energy conservation
12Iω2=Un−Ut\dfrac{1}{2}{I\omega }^{2}={U}_{n}-{U}_{t}
=−MBcos60∘−(−MB)=-MBcos60^{\circ}-(-MB)
MB2=12Iω2\dfrac{MB}{2}=\dfrac{1}{2}{I\omega }^{2}
20×42=12(08)m2\dfrac{20\times 4}{2}=\dfrac{1}{2}(08){m}^{2}
100=ω2100={\omega }^{2}
ω=10rad\omega =10rad

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