A charged particle (charges = q, mass = m) is rotating in a circle of radius R with uniform speed V ratio of its magnetic moment `(mu)` to the angular momentum (L) is

Options

A. `(q)/(2m)`
B. `(q)/(m)`
C. `(q)/(4m)`
D. `(2q)/(m)`

Answer

a

Explanation

The megnetic moment of charge, `mu = n//a`

and angular momentum of charge,
L= m.v.R
Here, n = 1
current `I = (q)/(T)`
Time-peroid, `T = (2 pi R)/(v)`
Equivalent current `I = (q)/(2 pi R//v) = (q.v)/(2 pi R)`
Area of loop or circle, `A = pi R^(2)`
`:. mu = 1 xx (q')/(2 pi R) xx pi RR^(2) = (qvR)/(2)`
`implies L = I omega = mR^(2) xx (v)/(R ) = mvR`
i = moment of inertia of loop
`:. (mu)/(L) = (niA)/(mvR) = (qvR//2)/(mvR) = (q)/(2m)