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Franz Ernst Neumann developed a mathematical theory of electromagnetic induction relating the induced response to the geometry of two electrical circuits. In modern notation, their mutual inductance $M$ enters the linked flux as $MI$, and a changing linked flux produces electromotive force $-d(MI)/dt$. Moving either circuit can change $M$, connecting a mechanical displacement with an induced electrical response. Maxwell's account identifies this induction theory as a mathematical counterpart to Ampère's treatment of the forces between currents.^[ref]

A physical property tensor must be invariant under every symmetry operation of the material's point group. For a polar rank-$r$ tensor, $T_{i_1\dots i_r}=R_{i_1{j}_1}\cdots R_{i_r{j}_r}{T}_{j_1\dots j_r}$. Taking $R=-I$ proves that an odd-rank polar tensor vanishes in a centrosymmetric material. A susceptibility of order $n$ has rank $n+1$, so local bulk even-order electric-dipole response is forbidden there. The name refers to Franz Ernst Neumann.