We predict the existence of large electric fields near the surface of
superconducting bodies of ellipsoidal shape of dimensions comparable to the
penetration depth. The electric field is quadrupolar in nature with significant
corrections from higher order multipoles. Prolate (oblate) superconducting
ellipsoids are predicted to exhibit fields consistent with negative (positive)
quadrupole moments, reflecting the fundamental charge asymmetry of matter.Comment: To be published in Phys.Rev.Let