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The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.
Maxwell's theorem is the following statement about triangles in the plane. ... Daniel Pedoe: Geometry: A Comprehensive Course. Dover, 1970, pp. 35–36, 114–115;
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.
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl 1,3 (R), or equivalently the geometric algebra G(M 4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and ...
These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime. But because general relativity dictates that the presence of electromagnetic fields (or energy / matter in general) induce curvature in spacetime, [ 1 ] Maxwell's equations in flat ...
The Kerr–Newman metric describes the spacetime geometry around a mass which is electrically charged and rotating. It is a vacuum solution which generalizes the Kerr metric (which describes an uncharged, rotating mass) by additionally taking into account the energy of an electromagnetic field, making it the most general asymptotically flat and stationary solution of the Einstein–Maxwell ...
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.
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.. For example, in the framework of special relativity, the Maxwell equations have the same form in all inertial frames of reference.