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Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction ...
Faraday's law states that the emf is also given by the rate of change of the magnetic flux: where is the electromotive force (emf) and ΦB is the magnetic flux. The direction of the electromotive force is given by Lenz's law. The laws of induction of electric currents in mathematical form was established by Franz Ernst Neumann in 1845.
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 most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as E(x, y ...
Maxwell's equations were an essential inspiration for the development of special relativity. Possibly the most important aspect was their denial of instantaneous action at a distance. Rather, according to them, forces are propagated at the velocity of light through the electromagnetic field. [28]: 189.
In addition, the Maxwell–Faraday equation states =. These represent two of Maxwell's four equations and they intricately link the electric and magnetic fields together, resulting in the electromagnetic field. The equations represent a set of four coupled multi-dimensional partial differential equations which, when solved for a system ...
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