JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Magnetic Effects of Current

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

B

. The magnetic moment of this moving particle:

Answer: (D)

Solution

A charge

q

circling at radius

r = \frac{m v}{q B}

behaves like a current loop. Its magnetic moment has magnitude

I A = \frac{q}{2 π r / v} \cdot π r^{2} = \frac{q v r}{2} = \frac{q v}{2} \cdot \frac{m v}{q B} = \frac{m v ^{2}}{2 B}

. The sense of circulation makes this moment oppose the applied field, so in vector form

M = - \frac{m v ^{2} B}{2 B ^{2}}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option