An insulating thin rod of length $l$ has a linear charge density $\rho \left( x \right) = {\rho _0}\,\frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second, then the time averaged magnetic moment of the rod is
JEE MAIN 2019, Diffcult
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$\mathrm{dM} =\mathrm{di} \mathrm{A} $
$=\left(\frac{\mathrm{d} \mathrm{q} \omega}{2 \pi}\right) \pi \mathrm{x}^{2} $
$=(\rho \mathrm{d} \mathrm{x}) \frac{\omega}{2 \pi} \pi \mathrm{x}^{2} $
$\mathrm{M} =\int_{0}^{\mathrm{L}} \mathrm{dM}$
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