Axion Induced Oscillating Electric Dipole Moments

The axion electromagnetic anomaly induces an oscillating electric dipole for {\em any} static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low energy theorem which is a consequence of the space-time dependent cosmic background field of the axion in the limit that it is only locally time dependent $(\overrightarrow{\beta }=0)$. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\sim {10}^{-32}$ e-cm, three orders of magnitude above the nucleon, and within four orders of magnitude of the present standard model DC limit. This may suggest sensitive new experimental venues for the axion dark matter search.