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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.
In fact, Maxwell's equations were crucial in the historical development of special relativity. However, in the usual formulation of Maxwell's equations, their consistency with special relativity is not obvious; it can only be proven by a laborious calculation. For example, consider a conductor moving in the field of a magnet. [8]
The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws. Maxwell's derivation of the electromagnetic wave equation has been replaced in modern physics by a much less cumbersome method ...
Maxwell's continuous field theory was very successful until evidence supporting the atomic model of matter emerged. Beginning in 1877, Hendrik Lorentz developed an atomic model of electromagnetism and in 1897 J. J. Thomson completed experiments that defined the electron. The Lorentz theory works for free charges in electromagnetic fields, but ...
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.
The electromagnetic spectrum. Together, Maxwell's equations provide a single uniform theory of the electric and magnetic fields and Maxwell's work in creating this theory has been called "the second great unification in physics" after the first great unification of Newton's law of universal gravitation. [17]
This electromagnetic field is a source-free solution of the Maxwell field equations on the particular curved spacetime defined by the metric tensor above. It is a null solution, and it represents a transverse sinusoidal electromagnetic plane wave with amplitude q and frequency ω, traveling in the e 1 direction. When one
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.