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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.
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.
The final form of Maxwell's equations was published in 1865 A Dynamical Theory of the Electromagnetic Field, [8] in which the theory is formulated in strictly mathematical form. In 1873, Maxwell published A Treatise on Electricity and Magnetism as a summary of his work on electromagnetism.
In 1864 James Clerk Maxwell of Edinburgh announced his electromagnetic theory of light, which was perhaps the greatest single step in the world's knowledge of electricity. [123] Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when On Faraday's lines of force [ 124 ] was read to the Cambridge ...
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. [1] Physicist Freeman Dyson called the publishing of the paper the "most important event of the nineteenth century in the history of the physical sciences."
The electromagnetic field admits a coordinate-independent geometric description, and Maxwell's equations expressed in terms of these geometric objects are the same in any spacetime, curved or not. Also, the same modifications are made to the equations of flat Minkowski space when using local coordinates that are not rectilinear.
An exception was James Clerk Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. [9] [10] [11] In Maxwell's model, 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 slightly different from ...
Electromagnetic waves are predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. There are nontrivial solutions of the homogeneous Maxwell's equations (without charges or currents), describing waves of changing electric and magnetic fields. Beginning with Maxwell's equations in free space: