An insulating thin rod of length \( l \) has a linear charge \( \ma...

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An insulating thin rod of length \( l \) has a linear charge
\( \mathrm{P} \) density \( \rho(x)=\rho_{0} \frac{x}{l} \) on it. The rod is rotated about

W an axis passing through the origin \( (x=0) \) and perpendicular to the rod. If the rod makes \( n \) rotations per seconds, then the time averaged magnetic moment of the rod is
(1) \( \frac{\pi}{4} n \rho_{0} l^{3} \)
(2) \( \pi n \rho_{0} l^{2} \)
\( \theta \)
(3) \( \frac{\pi}{3} n \rho_{0} l^{3} \)
(4) \( n \rho_{0} l^{3} \)
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