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 M axwell, all charge depended on the electric field. Charge was induced and polarizat ion was described by a single dielectric constant. Electrons, permanent charge, and polarization are important when matter is involved. Polarization of matter cannot be des cribed by a single dielectric constant 𝜀r with reasonable realism today when applications involve 10−10 sec. Only vacuum is well described by a single dielectric constant 𝜀0 . Here, Maxwell's equations are rewritten to include permanent charge and any type of polarization. Rewritin g is in one sense petty , and in another sense profound , in either case presumptuous . Either petty or profound , rewriting confirm s the legitimacy of electrodynamics that includes permanent charge and realistic polarization. One cannot be sure ahead of time that a theory of electro dynamics without electrons or (permanent, field independent) 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) t hat are not in the theor y 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 𝜀0𝜕𝐄𝜕𝑡⁄) 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) Classical chemical kinetics is seen to need revision to conserve current. 3 Introduc tion. Maxwell ’s equations describe the relation of charge and electric forces almost perfectly [1]. Yet Maxwell ’s equations (as written by Maxwell and Maxwellians before 1897 [2-7]) do not include the electron and its charge. For Maxwell , charge always depended on the electric field. Charge was induced. He did not know of charge that was independent of potential or the electric field [2, 3, 7] , p. 36 of [1]. Permanent charge —fixed in magnitude, independent of the electric field —was not part of electrodynamics (for Maxwellians, mostly in the UK , many at Trinity Cambridge ) until J.J. Thomson discovered the charge on the electron in 1897 [8]. Just four years earlier , Thomson had described electrodynamics without charge [4]. Other physicists had other opinions , including Weber, Helmholtz, Neumann, Clausius, and Kirchhoff [5-7, 9]. The question is why can traditional Maxwell equations without electrons or permanent charges correctly describe an electrical world with electrons , even though that electrical world contains many charges that are permanent and do not depend on the electric field? The answer is that the Maxwell equations corre ctly describe the relation of field to charge . Where the properties of charge itself are involved, the equations are incomplete and misleading , and in that sense incorrect1 [10, 11] . The properties and nature of charge are crucial in important applications, for example, those involving ions in ionic solutions. Almost all biology [12-15] and electrochemistry [16-32] occurs in ionic solutions , along with much of biochemistry and classical chemistry. Ionic solutions consist of permanent charges —the ions but also perhaps in the solvent molecule i tself—and so Maxwell’s classical equations cannot deal with them, since those equations do not include permanent charges. Maxwell’s original equations cannot deal with the role of ions in biology or electrochemistry. Maxwell’s equations use a severely over simplified description of polarization . Maxwell’s equations , as originally written, also have difficulty with the polarization (i.e., dielectric) charge in matter that is induced by electric field s. When an electric field is 1 If the word ‘incorrect’ seems too harsh, see p. 4 to read similar characterizatio ns by two Nobel Laureates in Physics . How else would one characterize a theory of gravitation that did not include mass ? How else would one characterize a theory of gravitation that dealt with the induced motion (‘polarization’) of the oceans, as revealed by tides [10,11] , and did not deal with mass itself? 4 applied, local forces are large enough to distort distribution s of charge within atoms and molecules or perturb them in other ways, e.g., by rotating molecules with asymmetrical permanent charge like water, H2O=𝐇+0.5δ 𝐎−1.0δ 𝐇0.5δ; δ≅0.4. Permanent charge moves in an electric field and that movement is called polarization. When local electric fields are zero, polarization is zero, in our u se of that word. Maxwell’s equations describe induced charge and polarization with a single dielectric constant . They use one real number 𝜀𝑟≥1. Only the polarization and dielectric properties of a vacuum can be realistically described by a dielectric constant that is a single real positive number . Only in a vacu um does 𝜀𝑟=1. Polarization charge in real materials varies dramatically with time. In our electronic devices , time scales range from 10−10 to >100 sec [33-50]. Polarization i n ionic solutions varies by a factor of ~ 40 in the time range linking atomic motions to macroscopic movements 10−15 to >100 sec, estimated by the effective dielectric coefficient measured in innumerable experiments . This time scale is used in hundreds of simulations of molec ular dynamics of proteins every day. L inkage of atomic motion and macroscopic function is a central issue in molecular biology and electrochemistry because atomic structure controls macroscopic f unction in life and technology .