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Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation, these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays.
[24] [25] Maxwell deals with the motion-related aspect of electromagnetic induction, v × B, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, F = q ( E + v × B ) , which sits adjacent to Maxwell's equations and bears the name Lorentz force ...
A subset of the constants of motion are the integrals of motion, or first integrals, defined as any functions of only the phase-space coordinates that are constant along an orbit. Every integral of motion is a constant of motion, but the converse is not true because a constant of motion may depend on time. [ 2 ]
The motion is exactly consistent in these two different reference frames, but it mathematically arises in quite different ways. For this reason and others, it is often useful to rewrite Maxwell's equations in a way that is " manifestly covariant "—i.e. obviously consistent with special relativity, even with just a glance at the equations ...
Combination of spatial and temporal variables in Maxwell's theory required admission of a four-manifold. Finite light speed and other constant motion lines were described with analytic geometry. Orthogonality of electric and magnetic vector fields in space was extended by hyperbolic orthogonality for the temporal factor.
The Maxwell–Boltzmann distribution is a result of the kinetic theory of gases, which provides a simplified explanation of many fundamental gaseous properties, including pressure and diffusion. [3] The Maxwell–Boltzmann distribution applies fundamentally to particle velocities in three dimensions, but turns out to depend only on the speed ...
a) Maxwell's electrodynamics, as presented by Lorentz in 1895, was the most successful theory at this time. Here, the speed of light is constant in all directions in the stationary aether and completely independent of the velocity of the source;
Deriving equations of motion from an action has several advantages. First, it allows for easy unification of general relativity with other classical field theories (such as Maxwell theory), which are also formulated in terms of an action. In the process, the derivation identifies a natural candidate for the source term coupling the metric to ...