We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Za2 = ¿0 for a sufficiently small ¿0, where a denotes the fine structure constant. We show that, in the simultaneous limit Z ¿ 8, a ¿ 0 such that ¿ = Za2 is fixed, the ground state energy of the system is given by a two term expansion c1Z7/3 + c2(¿) Z2 + o(Z2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.