  We consider a Schr\"odinger operator $(h\mathbf D -\mathbf A)^2$ with a
positive magnetic field $B=\curl\mathbf A$ in a domain $\Omega\subset\R^2$. The
imposing of Neumann boundary conditions leads to spectrum below $h\inf B$. This
is a boundary effect and it is related to the existence of edge states of the
system. We show that the number of these eigenvalues, in the semi-classical
limit $h\to 0$, is governed by a Weyl-type law and that it involves a symbol on
$\partial\Omega$. In the particular case of a constant magnetic field, the
curvature plays a major role.
