Practical_Antenna_Handbook_0071639586
C h a p t e r 3 : A n t e n n a B a s i c s 89 Capacitor Figure 3.2 Charges on the plates of a capacitor. Direction of current flow angles to the current—namely, a circular field surrounding the conductor. Thus, magnetic fields and the currents that create them are always at right angles to each other. Similarly, the force on a moving electron (which constitutes a current, however small) from a magnetic field is proportional to the electron’s velocity (i.e., to the current in a wire) and always at right angles to its direction of travel. Thus, a magnetic field can cause a moving electron to change direction, but it cannot cause it to speed up or slow down! The strength and orientation of the magnetic field (usually represented by H) in a region of space is Direction of magnetic field Left hand Figure 3.3 Magnetic field around a halfwave antenna.
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-
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C h a p t e r 3 : A n t e n n a B a s i c s 89<br />
Capacitor<br />
<br />
<br />
<br />
<br />
Figure 3.2 Charges on the plates of a capacitor.<br />
Direction of<br />
current flow<br />
angles to the current—namely, a circular<br />
field surrounding the conductor.<br />
Thus, magnetic fields and the<br />
currents that create them are always<br />
at right angles to each other. Similarly,<br />
the force on a moving electron<br />
(which constitutes a current, however<br />
small) from a magnetic field is<br />
proportional to the electron’s velocity<br />
(i.e., to the current in a wire) and<br />
always at right angles to its direction<br />
of travel. Thus, a magnetic field can<br />
cause a moving electron to change<br />
direction, but it cannot cause it to<br />
speed up or slow down!<br />
The strength and orientation of<br />
the magnetic field (usually represented<br />
by H) in a region of space is<br />
Direction of magnetic<br />
field<br />
Left hand<br />
Figure 3.3 Magnetic field around a halfwave<br />
antenna.
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