A particle with charge q is moving along a circle of radius R with uniform speed v. The associated magnetic moment μ is given by:

Question

A particle with charge q is moving along a circle of radius R with uniform speed v. The associated magnetic moment μ is given by: (A) (1/2) v2 R (B) (1/4) qvR (C) (1/2) qvR (D) (1/2) q2 v R

Tardigrade Admin · Accepted Answer

N text persec =(1/ T )=( v /2 π R ) Current through circular orbit i =( q / T )=( vq /2 π R ) Magnetic moment ⇒ μ= IA =( vq /2 π R ) × π R 2=( vqR /2)

Q. A particle with charge $q$ is moving along a circle of radius $R$ with uniform speed $v$ . The associated magnetic moment $μ$ is given by:

$\frac{1}{2} v^{2} R$

$\frac{1}{4} q v R$

$\frac{1}{2} q v R$

$\frac{1}{2} q^{2} v R$

$N_{persec} = \frac{1}{T} = \frac{v}{2 π R}$
Current through circular orbit
$i = \frac{q}{T} = \frac{v q}{2 π R}$
Magnetic moment $\Rightarrow μ = I A$
$= \frac{v q}{2 π R} \times π R^{2} = \frac{v qR}{2}$

Q. A particle with charge q is moving along a circle of radius R with uniform speed v. The associated magnetic moment μ is given by:

21​v2R

41​qvR

21​qvR

21​q2vR