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BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 33
where the closed contour L is alike in Figure 1.6.8. Transforming step-by-step the linear integral
nd
on the right-hand side of (1.59) as well as (1.38) we obtain the integral form of 2 Maxwell’s
equation
∮ ∘ − ∬ ∘ = 0 (1.60)
The second integral term in (1.60) received the particular name, displacement current as the
time-varying source of magnetic field
= ∬ ∘ [A] (1.61)
It is measured in Amps the same way as standard electric current. A quick comparison of (1.60)
and (1.4) allows us to define the volume density of displacement current as
= ∬ ∘ � (1.62)
2
⁄
⁄
= () [V m ]
The existence of such kind of current was claimed by British scientist James Clerk Maxwell
between 1862 and 1864 and brought him the acclaim of being one of the greatest scientists of
all times. Maxwell was the first who formulated the equations bearing his name and, in the
course of time, his electromagnetic theory became one of the founding principles on which
modem physics and electrical engineering science is based. It is important to point out that the
displacement current makes the equations of electrodynamics consistent with charge
conservation law.
The most remarkable fact that the displacement current is not due to moving any charged
particles. Quite the opposite, it is proportional to the flux of the derivative of the displacement
field with respect to time in any medium including vacuum. Therefore, it is unnecessary to have
any wire or any other physical object for this current to be carried. Based on this fact Maxwell
predicted the equivalence of light and EM wave. His concept "has been the subject of both
admiration and controversy for more than a century" [29] despite the fact that just in a decade,
exactly in 1887, German scientist Heinrich Rudolf Hertz designed a brilliant set of instruments
and conclusively proved Maxwell's hypothesis. His experiments established that light and EM
waves were both a form of EM radiation obeying Maxwell’s equations. More than that, Hertz
created the first in the world antenna, Hertz’s dipole, and found out how such antenna helps the
electric and magnetic fields to detach themselves from wires and go free as Maxwell's waves.
The unit of frequency – cycles per second – was named the "Hertz" in his honor.
nd
We now temporally turn our attention away from 2 Maxwell’s equation to establish paramount
phenomena, the continuity of net current defined as the mixture of electric and displacement
current.
nd
1.6.16 Net Current Continuity and 2 Maxwell’s Equation
Let us come back to the electric current continuity equation (1.36) and replace the volume
charge density with the divergence (1.32) of the displacement vector D
0 = ∘ + = ∘ + ( ∘ ) = ∘ + ∘ (1.63)