A circular coil having 200 turns, area and carrying 100 current is placed in a uniform magnetic field of 1 T. Initially, the magnetic dipole moment was directed along . Amount of work, required to rotate the coil through 90° from its initial orientati

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Solution

Q.
A circular coil having 200 turns, $2.5 \times 10^{- 4} m^{2}$ area and carrying 100 $μ A$ current is placed in a uniform magnetic field of 1 T. Initially, the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$ . Amount of work, required to rotate the coil through 90° from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$ , is ____ $μ J$ . [2024]

Ans.
(5)

Work done by external magnetic field $Δ U = U_{f} - U_{i}$

Initially, $U_{i} = - M B \cos θ = - M B \cos 0 ° = - M B$

Finally, $U_{f} = - M B \cos 90 ° = 0$

The magnetic moment of coil, $M = N i A$

$M = (100 \times 10^{- 6}) \cdot (200) \cdot (2.5 \times 10^{- 4})$

Work, $W = Δ U = M B = (5 \times 10^{- 6}) (1) = 5 μ J$

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