A Dynamical Theory of the Electromagnetic Field
" A dynamical theory of the electromagnetic field " ( original title: "A dynamical theory of the electromagnetic field ") is the third official 1864 published by James Clerk Maxwell to electrodynamics. It is the publication in which the original four formulas of Maxwell's equations occurred the first time. The concept of displacement current, which he had introduced in 1861 in his publication On physical lines of force, he used to derive the electromagnetic wave equation.
Maxwell's original equations
In Part III of A dynamical theory of the electromagnetic field with the title " General equations of the electromagnetic field " (orig.: " General equations of the electromagnetic field " ) Maxwell formulated twenty equations. These were as Maxwell's equations known until the term was used for the set of four equations vectored by Oliver Heaviside, published in 1884 in On physical lines of force.
Heaviside wrote his version of Maxwell's equations in modern vector case. They contain only one of the original equations, the Gauss's law (G). Another of the four Heaviside equations is a fusion of Maxwell's Laws of Total Currents (A) and Ampère 's circuital law (C). This merger, which originally led by Maxwell himself in equation 112 in On physical lines of force, Ampere 's Circuital Law adds Maxwell's displacement current.
18 of the 20 original Maxwell 's equations can be summarized by vectorization in six equations. Each vector equation corresponds to three original in component form. Together with the two other equations in modern vector notation they form a set of eight equations:
Maxwell was not associated with a general materials properties; its original formulation presupposes linear, isotropic and non- dispersive ε ( permittivity) and μ (permeability). However, he discussed the possibility of anisotropic materials.
It is of particular interest that the Maxwell term in its equation ( D) for the " electromotive force " einfügte. This corresponds to the magnetic force per unit charge acting on a moving at the speed ladder. Equation ( D) effectively describes thus the Lorentz force. This equation is the first time before in equation (77 ) in the publication On physical lines of force for some time before Lorentz found this equation. Today, the Lorentz force is not treated in addition to the Maxwell equations, as an integral part thereof.
As Maxwell in his paper of 1864 herleitete the electromagnetic wave equation, he used the equation (D) instead of Faraday's law of electromagnetic induction, as it stands today in textbooks. However, Maxwell dropped the term in the derivation in equation (D).
Light as an electromagnetic wave
In A dynamical theory of the electromagnetic field, Maxwell uses the correction in the Ampère law under Part III of On physical lines of force. In Part VI of its publication Electromagnetic theory of light in 1864, he combined the displacement current with other equations of electromagnetism and received a wave equation with a rate that corresponded to the velocity of light. This, he commented:
" The consistency of the results suggest that light and magnetism of one and the same substance are caused and moving light as an electromagnetic disturbance through the field according to electromagnetic laws. ("The agreement of the results Seems to show that slight and magnetism are affections of the same substance, and that slight is an electromagnetic disturbance propagated through the field accor ding to electromagnetic laws. " ) "
Maxwell's derivation of the electromagnetic wave equation in modern physics has been replaced by a less laborious method, with a corrected version of Ampère law and Faraday's law of electromagnetic induction.
The modern derivation of the electromagnetic wave equation in vacuum begins with the Heaviside form of Maxwell's equation. Are written in Si units this:
Suppose the rotation of the rotation equations, we obtain:
With the identity of the vector equations
As with each of the spatial feature vector, we obtain the wave equations
With
As the vacuum speed of light.