  We present a detailed analysis of the scattering of charged particles by the
magnetic field of a long solenoid of constant magnetic flux and finite radius.
We study the relativistic and non-relativistic quantum and classical scenarios.
The classical limit of the perturbative quantum expressions, understood as the
Planck's limit (making $\hbar$ going to zero) is analyzed and compared with the
classical result. The classical cross section shows a general non-symmetric
behavior with respect to the scattering angle in contradistinction to the
quantum calculations performed so far. The various regimes analyzed show that
the quantum cross sections do not satisfy the correspondence principle: they do
not reduce to the classical result in any considered limit, an argument in
favor of the interpretation of the process as a purely quantum phenomenon. We
conclude that in order to restore the classical correspondence of the
phenomenon, a complete non-perturbative quantum calculation for a finite
solenoid radius is required.
