A moving coil galvanometer has $100$ turns and each turn has an area of $2.0 \mathrm{~cm}^2$. The magnetic field produced by the magnet is $0.01 \mathrm{~T}$ and the deflection in the coil is $0.05$ radian when a current of $10 \mathrm{~mA}$ is passed through it. The torsional constant of the suspension wire is $\mathrm{x} \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad}$. The value of $\mathrm{x}$ is____.
JEE MAIN 2024, Diffcult
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$\tau=\text { BINAsin } \phi$
$\mathrm{C} \theta=\mathrm{BINA} \sin 90^{\circ}$
$\mathrm{C}=\frac{\mathrm{BINA}}{\theta}=\frac{0.01 \times 10 \times 10^{-3} \times 100 \times 2 \times 10^{-4}}{0.05}$
$=4 \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad} .$
$\mathrm{x}=4$
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