Updating Maxwell with Electrons and Charge July 31 2019
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 ud835udf00r with reasonable realism today when applications involve 10u221210 sec. Only vacuum is well described by a single dielectric constant ud835udf000 . 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 ahead of time 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, (1) Maxwellu2019s equations seem universal and exact. (2) Polarization must be described explicitly to use Maxwellu2019s equations in applications. (3) Conservation of total current (including ud835udf000ud835udf15ud835udc04ud835udf15ud835udc61u2044) becomes exact, independent of matter, allowing precise definition of electromotive force EMF in circuits. (4) Kirchhoffu2019s current law becomes as exact as Maxwellu2019s equations themselves. (5) Classical chemical kinetics is seen to need revision to conserve current.
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