Period of revolution of charged particle q ,
T=circumference velocity
or T=2πR/v
Circulating current , I=q/T=q/(2πR/v)=qv/2πR
Therefore magnetic moment of charged particle ,
M=IA (where A=area of circular path)
M=(qv/2πR)(πR2)=(qvR/2) ..........eq1
Now , angular momentum of particle of mass m ,
L=mvR .............eq2
Dividivg eq1 by eq2 ,
ML=qvR/2mvR=q/2m