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Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such ...
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that emf (electromagnetic work done on a unit charge when ...
The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch.
Heaviside's version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations. In 1834 Heinrich Lenz formulated the law named after him to describe the "flux through the circuit". Lenz's law gives the direction of the induced emf and current resulting from electromagnetic induction.
For the field formulation of Maxwell's equations in terms of a principle of extremal action, see electromagnetic tensor. Often, the time derivative in the Faraday–Maxwell equation motivates calling this equation "dynamical", which is somewhat misleading in the sense of the preceding analysis.
Definition. The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1][2] f {\displaystyle F\ {\stackrel {\mathrm {def} } {=}}\ \mathrm {d} A.} Therefore, F is a differential 2-form — an antisymmetric rank-2 tensor field—on Minkowski space.
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
The Faraday paradox or Faraday's paradox is any experiment in which Michael Faraday 's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes: Faraday's law appears to predict that there will be zero electromotive force (EMF) but there is a non-zero EMF. Faraday's law appears to predict that ...