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NEOCLASSICAL THEORY OF INTERACTION 107

The graphs in Figure 2.10.1 present typical variation of () in radians and ln (|()|) over
the frequency. It is clear that the main
contribution to () comes from
ln (|()|) near ≈ ω due to the
0
resonant denominator in (2.111).
Therefore, a good estimation for (ω)
can be obtained if we really should
measure |(ω)| in the frequency range
around ω than elsewhere.
0
We stop our discussion at this point
asking the reader to attend more
comprehensive specialized publications
like [13].
Figure 2.10.1 Reflection coefficient () vs.
frequency
2.10.4 Eddy Current

Let us outline one more significant and amusing EM effect called the eddy current in conductors
discovered by French scientist Leon Foucault
Magnetic in 1851, and for this reason, sometimes it is
Field of Top called Foucault’s currents. In general, the eddy
Eddy Current or ‘whirlpool’ current is induced entirely
within suitable conducting materials (like
copper, iron or aluminum) by a relatively slow
varying in time electric or magnetic field. It
Top Eddy means that || ≫ | ∂ | or the
⁄
0
Current conductivity current much exceeds the
S displacement current. Alternatively, the
Magnetic Field of similar current appears when a conductive
N Fallen Magnet object moves or rotates relative to a nearby
Bottom permanent magnet or contrarily permanent
Eddy Current magnet moves or rotates nearby a stationary
conductive body. Eddy currents in power
transformer cores or ferromagnetic parts of
electric motor and generator represent lost
Magnetic Field power and are undesirable. On the other side,
of Bottom Eddy the eddy current has many beneficial
Current applications. It can produce remote heat in iron
base of cookware, detect invisible cracks and
Figure 2.10.2 Eddy current illustration cavities in metal bodies and tubes, sort
conductive materials, weld and inspect the
welding quality for high pressure water reactor tubes and aircraft body, test the metal coatings,
brake the motion of railroad train or roller coaster car with remarkable efficiency, etc. To
illustrate the eddy current phenomenon let us imagine that we drop a strong permanent magnet
inside a copper pipe as shown in Figure 2.10.2 . Evidently, as the falling disk magnet moves
34
away from the top end of the tube the reducing strength of magnetic inductance vector B(t) is

34 Public Domain Image, source: http://fweb.wallawalla.edu/class-wiki/index.php/Eddy_Current