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

The relation `mu_l` = -(e/2m) is in accordance with classical physics. It follows easily from the definitions of `mu_l` and l :
`mu_l = IA = (e/T) pi r^2`
`l = mvr = (2mpi r^2)/(T) ` ....(ii)
`(because v = 2pi r// T)`
where r is the radius of the circular orbit that the electron of mass m and charge (-e) completes in a time T.
clearly ` (mu_l)/(l) = (e )/(2m)`
An electron is a negatively charged particle and hence magnetic moment is opposite to that of orbital angular momentum . So we can put the negative sign .
`(m_l)/(l) = - (e )/(2m)`
Note: `mu_s//S` is constant and is equal to e/m i.e., twice the classically expected value .