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History of Maxwell's equations : ウィキペディア英語版
History of Maxwell's equations

In electromagnetism, one of the fundamental fields of physics, the introduction of Maxwell's equations (mainly in "''A Dynamical Theory of the Electromagnetic Field''") was one of the most important aggregations of empirical facts in the history of physics. It took place in the nineteenth century, starting from basic experimental observations, and leading to the formulations of numerous mathematical equations, notably by Charles-Augustin de Coulomb, Hans Christian Ørsted, Carl Friedrich Gauss, Jean-Baptiste Biot, Félix Savart, André-Marie Ampère, and Michael Faraday. The apparently disparate laws and phenomena of electricity and magnetism were integrated by James Clerk Maxwell, who published an early form of the equations, which modify Ampère's circuital law by introducing a displacement current term. He showed that these equations imply that light propagates as electromagnetic waves. His laws were reformulated by Oliver Heaviside in the more modern and compact vector calculus formalism he independently developed. Increasingly powerful mathematical descriptions of the electromagnetic field were developed, continuing into the twentieth century, enabling the equations to take on simpler forms by advancing more sophisticated mathematics.
==Relationships among electricity, magnetism, and the speed of light==

The relationships among electricity, magnetism, and the speed of light can be summarized by the modern equation:
:c = \frac), and determined that it should have units of velocity. They then measured this ratio by an experiment which involved charging and discharging a Leyden jar and measuring the magnetic force from the discharge current, and found a value ,〔(The story of electrical and magnetic measurements: from 500 B.C. to the 1940s, by Joseph F. Keithley, p115 )〕 remarkably close to the speed of light, which had recently been measured at by Hippolyte Fizeau in 1848 and at by Léon Foucault in 1850.〔 However, Weber and Kohlrausch did not make the connection to the speed of light.〔 Towards the end of 1861 while working on part III of his paper ''On Physical Lines of Force'', Maxwell travelled from Scotland to London and looked up Weber and Kohlrausch's results. He converted them into a format which was compatible with his own writings, and in doing so he established the connection to the speed of light and concluded that light is a form of electromagnetic radiation.〔"The Dictionary of Scientific Biography", by Charles Coulston Gillispie〕

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