Exact second virial coefficient for dipolar hard spheres

The second virial coefficient B2 for a fluid of dipolar hard spheres has been given several approximate forms valid in the limits of weak and strong interactions. They have been formulated as asymptotic expressions in a dimensionless interaction parameter λ. In this paper, B2 is determined exactly for all values of λ in both the three-dimensional case, where spheres may access the whole space and their dipole moments may be oriented in all directions, and in the quasi-two-dimensional case, where spheres have their centres bound to glide on a plane, while their dipole moments are still freely orientable in space.