Engineering Electrodynamics

2 Fundamental Equations of Electromagnetic Field

2.1 Primary Laws and Equations of Electromagnetism

From the moment when Maxwell, on the basis of the empirical laws discovered by Biot and Savart (1820) and Faraday (1831), formulated the general equations of electromagnetic field (1873) and introduced to these equations the hypothesis of displacement current, one could give up the traditional, historical way of teaching the electric and magnetic fields and, taking Maxwell’s equations as a starting point, derive from them in a deductive way all the basic equations of the macroscopic electrodynamics.

The first and the second Maxwell’s equations for bodies being in a relatively slow motion, with the velocity v ≪ c, have the form:

curl H=Jtota