The magnetic moment vectors `vecmu_s` and `vecmu_l` associated with the intrinsic spin angular momentum `vecS` and orbital angular momentum `vecl` respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy to be given by
`vecmu_s=-(e/m)vecS` and `vecmu_l=-((e)/(2m))vecl`
Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

Explanation

Out of the two relations given, only one is in accordance with classical physics. This is
Magnetic moment, `vecmu_l=-((e)/(2m))vecl`
It follows from the definitions of `mu_l` and `l`.
`mu_l=iA=(-e/T)pir^2` …(i)
Angular momentum, `l=mvr=m((2pir)/(T))r` ...(ii)
where r is the radius of the circular orbit, which the electron of mass m and charge `(-e)` completes in time T.
Divide (i) by (ii), `(mu_l)/(l)=(-e)/(T)pir^2xx(T)/(m2pir^2)=(-e)/(2m)`
`:. vecmu_l=((-e)/(2m))vecl`
Clearly `vecmu_l` and `vecl` will be antiparallel (both being normal to the plane of the orbit)
In contrast, `(mu_s)/(S)=e/m`. It is obtained on the basis of quantum mechanics.