  We consider the three-dimensional Laplacian with a magnetic field created by
an infinite rectilinear current bearing a constant current. The spectrum of the
associated hamiltonian is the positive half-axis as the range of an infinity of
band functions all decreasing toward 0. We make a precise asymptotics of the
band function near the ground energy and we exhibit a semi-classical behavior.
We perturb the hamiltonian by an electric potential. Helped by the analysis of
the band functions, we show that for slow decaying potential, an infinite
number of negative eigenvalues are created whereas only finite number of
eigenvalues appears for fast decaying potential. Our results show different
borderline type conditions that in the case where there is no magnetic field.
