Two particles , each of mass m and charge q , are kept at the two ends of a light rod of length 2l and is rotated with a uniform angular velocity about the vertical axis passing through the centre of the rod . Determine the ratio of the magnetic moment and the angular momentum of the combination with respect to the centre of the rod .

Explanation

Radius of the path described = l .
If the angular velocity = `omega, "time period", T=(2pi)/(omega)`.
In this duration of time , the amount of charge flowing through any point of the orbit = 2q .
So , the charge flowing per second
= effective current `(I)=(2q)/(T)=(qomega)/(pi)`
`therefore` Magnetic moment , `p_(m)=IA=(qomega)/(pi).pil^(2)=qomegal^(2)`
and angular momentum , `L=(2m)l^(2)omega=2momegal^(2)`
Therefore, `(p_(m))/(L)=(q)/(2m)`