We present a general description of electromagnetic RR interactions between pairs of magnetically dual D-branes, focusing on the interaction of a magnetically charged brane with an electrically charged one. In the boundary state formalism, it turns out that while the electric-electric and/or magnetic-magnetic interaction corresponds to the usual RR even spin structure, the magnetic-electric interaction is described by the RR odd spin structure. As representative of the generic case of a dual pair of p and 6-p-branes, we discuss in detail the case of the self-dual 3-brane wrapped on a T-6/Z(3), which looks like an extremal dyonic black hole in four dimensions. (C) 1998 Elsevier Science B.V.