A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

Question

A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on (A) ω and q (B) ω, q and m (C) q and m (D) ω and m

Tardigrade Admin · Accepted Answer

The effective current i=(q ω/2 π) and A=π r2. Magnetic moment M=i A=(1/2) q ω r2 Angular moment L=I ω=m r2 ω ⇒ (M/L)=(q/2 m)

Q. A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $ω$ . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

$ω$ and $q$

$ω, q$ and $m$

$q$ and $m$

$ω$ and $m$

The effective current $i = \frac{q ω}{2 π}$ and $A = π r^{2}$ .
Magnetic moment $M = i A = \frac{1}{2} q ω r^{2}$
Angular moment $L = I ω = m r^{2} ω$
$\Rightarrow \frac{M}{L} = \frac{q}{2 m}$

Q. A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

ω and q

ω,q and m

q and m

ω and m