  We present a relativistic quantum calculation at first order in perturbation
theory of the differential cross section for a Dirac particle scattered by a
solenoidal magnetic field. The resulting cross section is symmetric in the
scattering angle as those obtained by Aharonov and Bohm (AB) in the string
limit and by Landau and Lifshitz (LL) for the non relativistic case. We show
that taking pr_0\|sin(\theta/2)|/\hbar<<1 in our expression of the differential
cross section it reduces to the one reported by AB, and if additionally we
assume \theta << 1 our result becomes the one obtained by LL. However, these
limits are explicitly singular in \hbar as opposed to our initial result. We
analyze the singular behavior in \hbar and show that the perturbative Planck's
limit (\hbar -> 0) is consistent, contrarily to those of the AB and LL
expressions. We also discuss the scattering in a uniform and constant magnetic
field, which resembles some features of QCD.
