Question 244 of 276

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

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Answer: 5

We know
$\begin{aligned}
\mathrm{W}_{\text {ext }} & =\Delta \mathrm{U}+\Delta \mathrm{KE} \quad(\text { P.E. }=-\overrightarrow{\mathrm{M}} \cdot \overrightarrow{\mathrm{B}}) \\
& =-\overrightarrow{\mathrm{M}} \cdot \overrightarrow{\mathrm{B}}_{\mathrm{f}}+\overrightarrow{\mathrm{M}} \cdot \overrightarrow{\mathrm{B}}_{\mathrm{i}}+0 \\
& =-\mathrm{MB} \cos 90+\mathrm{MB} \cos 0 \\
& =\mathrm{MB} \\
& =\mathrm{NIAB} \\
& =200 \times 100 \times 10^{-6} \times \frac{5}{2} \times 10^{-4} \times 1=5 \mu \mathrm{J}
\end{aligned}$