1 research outputs found
Updating Maxwell with Electrons, Charge, and More Realistic Polarization
Maxwell's 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 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 with reasonable realism today. Only
vacuum is well described by a single dielectric constant . 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. Rewriting confirms the
legitimacy of electrodynamics. One cannot be sure ahead of time that a theory
of electrodynamics without electrons or permanent charge (like Maxwell's
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) Maxwell's equations seem
universal and exact. (2) Polarization must be described explicitly to use
Maxwell`s equations in applications. (3) Conservation of total current
(including displacement current )
becomes exact, independent of matter, allowing precise definition of
electromotive force EMF in circuits.(4) Kirchhoff's current law becomes as
exact as Maxwell`s equations themselves. (5) Conservation of total current
needs to be satisfied in a wide variety of systems where it has not
traditionally received much attention. (6) Classical chemical kinetics is seen
to need revision to conserve current.Comment: Version 2 & 3 have typos corrected, minor revisions in text and
references. Versions 4-6 have some new ideas. Version 7 has an important typo
corrected on p. 13, after eq