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In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics. [9] Maxwell built a simple flywheel model of electromagnetism, and Boltzmann built an elaborate mechanical model ("Bicykel") based on Maxwell's flywheel model, which he used for lecture demonstrations. [10]
The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.
The structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem).
In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's lines of force. Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/56 when "On Faraday's Lines of Force" [ 2 ] was read to the Cambridge Philosophical Society .
Maxwell's equations (in partial differential form) are modified to central-difference equations, discretized, and implemented in software. The equations are solved in a cyclic manner: the electric field is solved at a given instant in time, then the magnetic field is solved at the next instant in time, and the process is repeated over and over ...
The law was first [1] formulated by Joseph-Louis Lagrange in 1773, [2] followed by Carl Friedrich Gauss in 1835, [3] both in the context of the attraction of ellipsoids. It is one of Maxwell's equations, which forms the basis of classical electrodynamics. [note 1] Gauss's law can be used to derive Coulomb's law, [4] and vice versa.
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Maxwell's equations, when they were first stated in their complete form in 1865, would turn out to be compatible with special relativity. [1] Moreover, the apparent coincidences in which the same effect was observed due to different physical phenomena by two different observers would be shown to be not coincidental in the least by special ...