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Maxwell's equations on a plaque on his statue in Edinburgh. 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.
These equations taken together are as powerful and complete as Maxwell's equations. Moreover, the problem has been reduced somewhat, as the electric and magnetic fields together had six components to solve for. [1] In the potential formulation, there are only four components: the electric potential and the three components of the vector potential.
The paper was key in establishing the classical theory of electromagnetism. [3] Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and also deduces that light is an electromagnetic wave.
In 1861, James Clerk Maxwell synthesized all the work to date on electrical and magnetic phenomena into a single mathematical theory, from which he then deduced that light is an electromagnetic wave. Maxwell's continuous field theory was very successful until evidence supporting the atomic model of matter emerged.
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.
The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v , with respect to a magnet is calculated in the frame of reference of the magnet and in the ...
James Clerk Maxwell FRS FRSE (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician [1] who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon.
Lorentz force on a charged particle (of charge q) in motion (velocity v), used as the definition of the E field and B field. Here subscripts e and m are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths.