Practical_Antenna_Handbook_0071639586

90 P a r t I I : F u n d a m e n t a l s
called the flux density, B. For an infinitely long, straight wire carrying a steady current I,
the magnitude of the flux density at a point located a distance R from the wire is
B = µ I
(3.16)
2πR
where m is the permeability of the medium surrounding the current-carrying wire. In any
region of permeability, m, B, and H are related by
B = µ H (3.17)
With the exception of ferromagnetic materials, most permeabilities for common
media are very close to that of a vacuum, m 0 = 400p × 10 –9 H/m (henries per meter), or,
more commonly, m 0 = 400p nH/m. The permeabilities of other media are expressed
relative to m 0 by
µ = µ r
µ o
(3.18)
In ferromagnetic materials, m r ranges from a few hundred for cobalt and nickel to
5000 for iron and 100,000 or more for specialty magnetic materials such as mu-metal and
permalloy. The effect of high permeability is to intensify the magnetic field created by a
given current. Thus, power and audio transformers employ iron cores for highly efficient
coupling between primary and secondary windings, and RF transformers often
use ferrite cores called toroids for the same purpose, as we shall see in Chap. 24.
Displacement Current and Maxwell’s Equations
If you have ever been running an appliance, such as a vacuum cleaner, in your home
and accidentally unplugged the cord from the wall, you know the appliance immediately
stopped. Its electrical circuit had been broken, and no current could flow to its
motor. One of the earliest questions asked about capacitors was: How can (the temporary
charging) current flow in the wires connecting the capacitor plates to the battery
when the circuit is always broken in the space between the plates of the capacitor? A
Scot, James Clerk Maxwell, answered this question in 1861, when he proposed the existence
of a displacement current (in contrast to the conduction current in a wire) in the space
between the plates. This current is the same I = CDV/Dt already mentioned in our definition
of a capacitor.
Because the displacement current was unaffected by locating the capacitor plates in
a vacuum, Maxwell concluded there must be some invisible yet material medium permeating
all of space. He called this medium the æther, and it took scientists another half
century to conclude there was no such thing! Nonetheless, the displacement current
ultimately allowed Maxwell to show that a changing electric field creates a magnetic
field and a changing magnetic field creates an electric field. This created symmetric
cross-coupling terms to be added to then-existing equations that purported to describe
the relationship between electric and magnetic fields, and allowed Maxwell to summarize
all the important characteristics of electromagnetism in a family of interrelated
equations. Once derived and written down on paper, the solutions to these equations
were recognized by Maxwell and other scientists and mathematicians of the day as
being of the same form as those describing the propagation of sound waves and other
mechanical vibrations through media such as air and water.
Maxwell summarized all that he knew about electromagnetism in his Treatise of
1865, and it was there that he predicted, purely on the basis of his mathematical equa-