Additions and Corrections to ELECTRICITY and MAGNETISM by Oleg D. Jefimenko Page 96, Fig. Add d<
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Electricity and Magnetism : An Introduction to the Theory of Electric and Magnetic Fields
In the typical expressions for Maxwell’s equations there is no doubt that both sides are equal to each other, but as Jefimenko notes, ” Jefimenko, Solutions of Maxwell’s equations for electric and magnetic fields in arbitrary mediaAmerican Journal of Physics 60 10— The electric field is written in a slightly different – but completely equivalent – form.
Covariant formulation Electromagnetic tensor stress—energy tensor Four-current Electromagnetic four-potential. This page was last edited on 16 Marchat GriffithsMark A. In electromagnetismJefimenko’s equations named after Oleg D.
Jefimenko’s equations – Wikipedia
These equations are the time-dependent generalization of Coulomb’s law and the Biot—Savart law to electrodynamicswhich were originally true only for electrostatic and magnetostatic fields, and steady currents. JefimenkoElectricity and Magnetism: Part of a series of articles about Electromagnetism Electricity Magnetism Electrostatics.
There are similar expressions electriciity D and H. There is a widespread interpretation of Maxwell’s equations indicating that spatially varying electric and magnetic fields can cause each other to change in time, thus giving rise to a propagating electromagnetic wave  electromagnetism.
In other words, the left side of each equation is actually “caused” by the right side, unlike the normal differential expressions for Maxwell’s equations where both sides take place simultaneously.
Views Read Edit View history. Retrieved from ” https: Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: Charge density and current density are creating them both.
Electricity and Magnetism by Jefimenko, Oleg D
Essential features of these equations are easily observed which is that the right hand sides involve “retarded” time which reflects the “causality” of the expressions. Electromagnetic tensor stress—energy tensor.
However, Jefimenko’s equations show an alternative point of view. JefimenkoCausality Electromagnetic Induction and Gravitation2nd ed.: Jefimenko give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay retarded time of the fields due to the finite speed of electricty and relativistic effects.
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Hence, it is impossible for E and B fields to be “creating” each other. As pointed out by McDonald,  Jefimenko’s equations seem electrucity appear first in in the second edition of Panofsky and Phillips’s classic textbook.