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The above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the (possibly atomic-level) charges and currents present. This is sometimes called the "general" form, but the macroscopic version below is equally general, the difference being one of bookkeeping.
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]
In physics, the electric displacement field (denoted by D), also called electric flux density or electric induction, is a vector field that appears in Maxwell's equations.It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field.
Interface conditions describe the behaviour of electromagnetic fields; electric field, electric displacement field, and the magnetic field at the interface of two materials. The differential forms of these equations require that there is always an open neighbourhood around the point to which they are applied, otherwise the vector fields and H ...
Since the potentials satisfy Maxwell's equations, the fields derived for point charge also satisfy Maxwell's equations. The electric field is expressed as: [29] (,) = (() | | + (() ˙) | |) = where is the charge of the point source, is retarded time or the time at which the source's contribution of the electric field originated, () is the ...
In part III of the paper, which is entitled "General Equations of the Electromagnetic Field", Maxwell formulated twenty equations [1] which were to become known as Maxwell's equations, until this term became applied instead to a vectorized set of four equations selected in 1884, which had all appeared in his 1861 paper "On Physical Lines of Force".
Similarly, taking divergence of equation [E] gives conservation of electric charge, =, which, Maxwell points out, is true only if the total current includes the variation of electric displacement. Lastly, combining equation [ A ] and equation [ E ] , the formula ∇ 2 A = 4 π μ C {\displaystyle \nabla ^{2}\mathbf {A} =4\pi \mu \mathbf {C ...
He applied a technique which is now generally called second quantization, [2] although this term is somewhat of a misnomer for electromagnetic fields, because they are solutions of the classical Maxwell equations. In Dirac's theory the fields are quantized for the first time and it is also the first time that the Planck constant enters the ...