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Electromagnetism

The discoveries of Hans Christian Ørsted on electromagnetism and Michael Faraday on electromagnetic induction drew Gauss's attention to these matters. Gauss and Weber found rules for branched electric circuits, which were later found independently and firstly published by Gustav Kirchhoff and benamed after him as Kirchhoff's circuit laws, and made inquiries on electromagnetism. They constructed the first electromechanical telegraph in 1833, and Weber himself connected the observatory with the institute for physics in the town centre of Göttingen, but they did not care for any further development of this invention for commercial purposes.

Gauss's main theoretical interests in electromagnetism were reflected in his attempts to formulate quantitive laws governing electromagnetic induction. In notebooks from these years, he recorded several innovative formulations; he discovered the idea of vector potential function (independently rediscovered by Franz Ernst Neumann in 1845), and in January 1835 he wrote down an "induction law" equivalent to Faraday's law, which stated that the electromotive force at a given point in space is equal to the instantaneous rate of change (with respect to time) of this function.

Gauss tried to find a unifying law for long-distance effects of electrostatics, electrodynamics, electromagnetism, and induction, comparable to Newton's law of gravitation, but his attempt ended in a "tragic failure".