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 $1 \mathrm{~T}$. 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 $\overrightarrow{\mathrm{M}}$ becomes perpendicular to $\vec{B}$, is. . . . $\mu \mathrm{J}$.
JEE MAIN 2024, Diffcult
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