Aharonov and Bohm constructed a wave function describing scattering of electrons by an impenetrable solenoid, from which they derived a cross section of the form dσ/dϑ = g (ϑ)sin2(πα), where ϑ is the scattering angle and α is a coupling constant. A simplified version of their work is presented, together with an attempt to obtain by Born approximation the approximate expression dσ/dϑ ? g (ϑ) π2α2 small α. It is explained why such an attempt is unsuccessful.