A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with resect to normal axis then the magnetic moment of the loop is: (a) q ω r2 (b) 4/3 q ω r2 (c) 3/2 q ω r2 (d) 1/2 q ω r2

Answer: (d). Equivalent current: charge q passes a point once per period, I = q/T = (qω)/(2π). M = Iπ r² = (qω)/(2π)π r² So the answer is (d) 1/2qω r².

A charge q is spread uniformly over an insulated loop of radius r. If… | JEE Main 2018 (16 Apr, Shift 1)

Q76JEE Main 2018 · 16 APR · SHIFT 1Medium

Current Loop as a Magnetic Dipole

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity $\omega$ with resect to normal axis then the magnetic moment of the loop is:

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Answer: (d)

Equivalent current: charge $q$ passes a point once per period, $I = \frac{q}{T} = \frac{q\omega}{2\pi}$ .
$M = I\pi r^2 = \frac{q\omega}{2\pi}\pi r^2$
So the answer is (d) $\frac{1}{2}q\omega r^2$ .

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