A charged particle going around in a circle can be considered to be a… | JEE Main 2020 (6 Sep, Shift 2)

Q62JEE Main 2020 · 6 SEP · SHIFT 2Medium

Current Loop as a Magnetic Dipole

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $\vec{B}$ . The magnetic moment of this moving particle:

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Answer: (b)

Radius $r = \frac{mv}{qB}$ ; equivalent current $I = \frac{qv}{2\pi r}$ .
$M = I\pi r^2 = \frac{qvr}{2} = \frac{qv}{2}\cdot\frac{mv}{qB} = \frac{mv^2}{2B}$
The induced moment always opposes $\vec{B}$ (for either sign of $q$ ), so $\vec{M} = -\frac{mv^2}{2B}\hat{B} = -\frac{mv^2\vec{B}}{2B^2}$ .
So the answer is (b).

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Current Loop as a Magnetic Dipole question from JEE Main 2020 (6 Sep, Shift 2)

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