= Franz Ernst Neumann
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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.<A Treatise on Electricity and Magnetism by James Clerk Maxwell>[Volume II, Part IV, Chapter III, sections 542–543 and the historical induction discussion; modern notation]{ref}
\Image[https://commons.wikimedia.org/wiki/Special:Redirect/file/Franz%20Ernst%20Neumann%20by%20Carl%20Steffeck%201886.jpg?width=250]
{title=Portrait of <Franz Ernst Neumann>}
{description=Carl Steffeck, 1886; Nationalgalerie Berlin, accession A I 376; faithful reproduction via Wikimedia Commons. Public-domain artwork: author died more than 100 years ago; faithful reproduction treated as public domain in the United States under Commons PD-Art. https://creativecommons.org/publicdomain/mark/1.0/[Source usage terms], via Wikimedia Commons.}
{source=https://commons.wikimedia.org/wiki/File:Franz_Ernst_Neumann_by_Carl_Steffeck_1886.jpg}
{width=250}
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