The mean inner potential of a solid is known to be proportional to its diamagnetic susceptibility. Superconductors exhibit giant diamagnetism. What does this say about the connection between superconductivity and mean inner potential? Nothing, according to the conventional theory of superconductivity. Instead, it is proposed that a deep connection exists between the mean inner potential, diamagnetism, and superconductivity: that they are all intimately linked to the fundamental charge asymmetry of matter. It is discussed how this physics can be probed experimentally and what the implications of different experimental findings would be for the understanding of superconductivity.