Relativistic electromagnetism is a physical phenomenon explained in electromagnetic field theory due to Coulomb's law and Lorentz transformations.
After Maxwell proposed the differential equation model of the electromagnetic field in 1873, the mechanism of action of fields came into question, for instance in the Kelvin’s master class held at Johns Hopkins University in 1884 and commemorated a century later.
The requirement that the equations remain consistent when viewed from various moving observers led to special relativity, a geometric theory of 4-space where intermediation is by light and radiation. The spacetime geometry provided a context for technical description of electric technology, especially generators, motors, and lighting at first. The Coulomb force was generalized to the Lorentz force. For example, with this model transmission lines and power grids were developed and radio frequency communication explored.
An effort to mount a full-fledged electromechanics on a relativistic basis is seen in the work of Leigh Page, from the project outline in 1912 to his textbook Electrodynamics (1940) The interplay (according to the differential equations) of electric and magnetic field as viewed over moving observers is examined. What is charge density in electrostatics becomes proper charge density and generates a magnetic field for a moving observer.
A revival of interest in this method for education and training of electrical and electronics engineers broke out in the 1960s after Richard Feynman’s textbook.
Rosser’s book Classical Electromagnetism via Relativity was popular, as was Anthony French’s treatment in his textbook which illustrated diagrammatically the proper charge density. One author proclaimed, "Maxwell — Out of Newton, Coulomb, and Einstein".
The use of retarded potentials to describe electromagnetic fields from source-charges is an expression of relativistic electromagnetism.
The question of how an electric field in one inertial frame of reference looks in different reference frames moving with respect to the first is crucial to understanding fields created by moving sources.
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The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another.
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called electrostatic force or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb, hence the name. Coulomb's law was essential to the development of the theory of electromagnetism and maybe even its starting point, as it allowed meaningful discussions of the amount of electric charge in a particle.
In physics (specifically in electromagnetism), the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force (in SI units) of It says that the electromagnetic force on a charge q is a combination of a force in the direction of the electric field E proportional to the magnitude of the field and the quantity of charge, and a force at right angles to the magnetic field B and the velocity v of the charge, proportional to the magnitude of the field, the charge, and the velocity.
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