The electric multipole expansion for a magic cube

Abstract

Recent studies of the rotational properties of magic cubes are extended to a corresponding electrical problem. While expecting the dipole moments of magic cubes to vanish, it was a surprise to find their quadrupole moments also vanished. These properties are shown to follow from the RCP (row, column, pillar) symmetry of the orthogonal line sums, namely the semi-magic property of the cubes, which opens up the conclusions to a much wider class of charge distributions.