  We consider non-interacting particles subject to a fixed external potential
$V$ and a self-generated magnetic field $B$. The total energy includes the
field energy $\beta \int B^2$ and we minimize over all particle states and
magnetic fields. In the case of spin-1/2 particles this minimization leads to
the coupled Maxwell-Pauli system. The parameter $\beta$ tunes the coupling
strength between the field and the particles and it effectively determines the
strength of the field. We investigate the stability and the semiclassical
asymptotics, $h\to0$, of the total ground state energy $E(\beta, h, V)$. The
relevant parameter measuring the field strength in the semiclassical limit is
$\kappa=\beta h$. We are not able to give the exact leading order semiclassical
asymptotics uniformly in $\kappa$ or even for fixed $\kappa$. We do however
give upper and lower bounds on $E$ with almost matching dependence on $\kappa$.
In the simultaneous limit $h\to0$ and $\kappa\to\infty$ we show that the
standard non-magnetic Weyl asymptotics holds. The same result also holds for
the spinless case, i.e. where the Pauli operator is replaced by the
Schr\"odinger operator.
