  The interaction potential of a two-dimensional system of excitons with
spatially separated electron-hole layers is considered in the strong magnetic
field limit. The excitons are assumed to have free dynamics in the $x$-$y$
plane, while being constrained or `polarized' in the $z$ direction. The model
simulates semiconductor double layer systems under strong magnetic field normal
to the layers. The {\em residual} interaction between excitons exhibits
interesting features, arising from the coupling of the center-of-mass and
internal degrees of freedom of the exciton in the magnetic field. This coupling
induces a dynamical dipole moment proportional to the center-of-mass magnetic
moment of the exciton. We show the explicit dependence of the inter-exciton
potential matrix elements, and discuss the underlying physics. The unusual
features of the interaction potential would be reflected in the collective
response and non-equilibrium properties of such system.
