Question:

A circular coil having 200 turns, 2.5×104 m22.5 \times 10^{-4} \text{ m}^2 area and carrying 100 μ\muA current is placed in a uniform magnetic field of 1 T. Initially the magnetic dipole moment (M\vec{M}) was directed along B\vec{B}. Amount of work, required to rotate the coil through 9090^\circ from its initial orientation such that M\vec{M} becomes perpendicular to B\vec{B}, is ________ μ\muJ.

Updated On: Mar 22, 2025
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Correct Answer: 5

Solution and Explanation

We know:

initial,final

Wext=ΔU+ΔKE(P.E.=MB) W_{\text{ext}} = \Delta U + \Delta KE \quad (\text{P.E.} = -\vec{M} \cdot \vec{B})

=MBcos90+MBcos0 = -MB \cos 90^\circ + MB \cos 0^\circ

Wext=MB W_{\text{ext}} = MB

=NIAB = NIAB

=200×100×106×2.5×104×1=5μJ = 200 \times 100 \times 10^{-6} \times 2.5 \times 10^{-4} \times 1 = 5 \, \mu\text{J}

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