Updating maxwell with electrons and charge Version 6
Maxwellu2019s equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on the electric field. Charge was induced and polarization was described by a single dielectric constant. Electrons, permanent charge, and polarization are important when matter is involved. Polarization of matter cannot be described by a single dielectric constant u03b5_(r )with reasonable realism today when applications involve 10^(-10) sec. Only vacuum is well described by a single dielectric constant u03b5_(0 ). Here, Maxwell's equations are rewritten to include permanent charge and any type of polarization. Rewriting is in one sense petty, and in another sense profound, in either case presumptuous. Either petty or profound, rewriting confirms the legitimacy of electrodynamics that includes permanent charge and realistic polarization. One cannot be sure that a theory of electrodynamics without electrons or (permanent, field independent) charge (like Maxwellu2019s equations as he wrote them) would be legitimate or not. After all a theory cannot calculate the fields produced by charges (for example electrons) that are not in the theory at all! After updating, tMaxwellu2019s equations seem universal and exact. tPolarization must be described explicitly to use Maxwellu2019s equations in applications. t Conservation of total current (including u03b5_0 u2202Eu2044u2202t) becomes exact, independent of matter, allowing precise definition of electromotive force EMF in circuits. tKirchhoffu2019s current law becomes as exact as Maxwellu2019s equations themselves. tConservation of total current needs to be satisfied in a wide variety of systems where it has not traditionally received much attention. tClassical chemical kinetics is seen to need revision to conserve current.
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