[en] We present a simple analysis that allows us to extract the leading mass dependence of the dipole moment of matter fermions that might be induced by new physics. We present explicit results for the supersymmetric model with broken R parity as an illustration. We show that the extra contributions to the electric dipole moment of fermions from Re_p interactions can occur only at the two-loop level, contrary to claims in the literature. We further find that unlike the generic leptoquark models, the extra contributions to the dipole moments of the leptons can only be enhanced by m_b/m_l and not by m_t/m_l relative to the expectations in the standard model. An interesting feature about this enhancement of these dipole moments is that it does not involve unknown mixing angles. We then use experimental constraints on the electric dipole moments of e^- and n to obtain bounds on (the imaginary part of) products of Re_p couplings, and show that bounds claimed in the literature are too stringent by many orders of magnitude. (c) 2000 The American Physical Society