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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 .
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
[10]: 510 An exception was James Clerk Maxwell, who in 1861–62 used Faraday's ideas as the basis of his quantitative electromagnetic theory. [10]: 510 [11] [12] In Maxwell's papers, the time-varying aspect of electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is ...
where = 4π×10 −7 V·s/(A·m) is the magnetic constant, and the direction of integration around is related to the direction of current by the right hand rule. The law can be expressed in terms of the current density J ( x ) {\displaystyle \mathbf {J} (\mathbf {x} )\,} through the surface S {\displaystyle S\,} instead of the total current I ...
Aluminium ring moved by electromagnetic induction, thus demonstrating Lenz's law. Experiment showing Lenz's law with two aluminium rings on a scales-like device set up on a pivot so as to freely move in the horizontal plane. One ring is fully enclosed, while the other has an opening, not forming a complete circle.
The anemometer of the earth inductor compass on the Spirit of St. Louis shows as a small "T" shape above the fuselage behind the wing. The Earth inductor compass (or simply induction compass [1]) is a compass that determines directions using the principle of electromagnetic induction, with the Earth's magnetic field acting as the induction field for an electric generator. [2]
In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects.
Reciprocity is useful in optics, which (apart from quantum effects) can be expressed in terms of classical electromagnetism, but also in terms of radiometry. There is also an analogous theorem in electrostatics, known as Green's reciprocity, relating the interchange of electric potential and electric charge density.