  This paper is concerned with Fr\"ohlich polarons subject to external
electromagnetic fields in the limit of large electron-phonon coupling. To
leading order in the coupling constant, $\sqrt\alpha$, the ground state energy
is shown to be correctly given by the minimum of the Pekar functional including
the electromagnetic fields, provided these fields in the Fr\"ohlich model are
scaled properly with $\alpha$. As a corollary, the binding of two polarons in
strong magnetic fields is obtained.
