A charged particle (charge `q`) is moving in a circle of radius `R` with unifrom speed `v`. The associated magnetic moment `mu` is given by

Options

A. ` ( q vR )/ (2 ) `
B. ` qv R ^ 2 `
C. ` ( q v R ^ 2) /( 2 ) `
D. ` qv R ^ 2 `

Answer

D

Explanation

As revolving charge is equivalent to a current , so ` I = q f = q xx ( omega ) /( 2pi ) `
But ` omega = ( v ) /( R) `
where ,R is radius of circle and v is uniform speed of charged particle.
Therefore, ` I = ( qv) /( 2pi R) `
Now, magnetic moment associated with charged particle is given by
`mu = IA = I xx pi R^ 2 `
or ` mu = (qv ) /( 2pi R ) xx pi R ^ 2 = q vR `