24.1

The Nature of Electromagnetic Waves

CONCEPTS AT A GLANCE In Section 13.3 we saw that energy is transported to us from the sun via a class of waves known as electromagnetic waves. This class includes the familiar visible, ultraviolet, and infrared waves. In Sections 18.6, 21.1, and 21.2 we studied the concepts of electric and magnetic fields. It was the great Scottish physicist James Clerk Maxwell (1831–1879) who showed that these two fields fluctuating together can form a propagating electromagnetic wave. The Concepts-at-a-Glance chart in Figure 24-1 emphasizes that we will now bring together our knowledge of electric and magnetic fields in order to understand this important type of wave.

Figure 24-1 CONCEPTS AT A GLANCE Electric and magnetic fields fluctuating together form an electromagnetic wave. The human body emits infrared electromagnetic waves, so called because they have wavelengths that are longer than the wavelength corresponding to the visible color red. This thermogram is that of a man with a sunburned back and head. Different colors show the intensities of the infrared waves emitted by different parts of the body, and these colors may be taken as an indication of temperature. The reds indicate higher temperatures while the blues signify lower temperatures. (Tony McConnell/SPL/Photo Researchers, Inc.)

Figure 24-2 illustrates one way to create an electromagnetic wave. The setup consists of two straight metal wires that are connected to the terminals of an ac generator and serve as an antenna. The potential difference between the terminals changes sinusoidally with time t and has a period T. Part a shows the instant , when there is no charge at the ends of either wire. Since there is no charge, there is no electric field at the point P just to the right of the antenna. As time passes, the top wire becomes positively charged and the bottom wire negatively charged. One-quarter of a cycle later , the charges have attained their maximum values, as part b of the drawing indicates. The corresponding electric field at point P is represented by the red arrow and has increased to its maximum strength in the downward direction.* Part b also shows that the electric field created at earlier times (see the black arrow in the picture) has not disappeared but has moved to the right. Here lies the crux of the matter: At distant points, the electric field of the charges is not felt immediately. Instead, the field is created first near the wires and then, like the effect of a pebble dropped into a pond, moves outward as a wave in all directions. Only the field moving to the right is shown in the picture for the sake of clarity.

Figure 24-2 In each part of the drawing, the red arrow represents the electric field produced at point P by the oscillating charges on the antenna at the indicated time. The black arrows represent the electric fields created at earlier times. For simplicity, only the fields propagating to the right are shown.

Parts c–e of Figure 24-2 show the creation of the electric field at point P (red arrow) at later times during the generator cycle. In each part, the fields produced earlier in the sequence (black arrows) continue propagating toward the right. Part d shows the charges on the wires when the polarity of the generator has reversed, so the top wire is negative and the bottom wire is positive. As a result, the electric field at P has reversed its direction and points upward. In part e of the sequence, a complete sine wave has been drawn through the tips of the electric field vectors to emphasize that the field changes sinusoidally.
Along with the electric field in Figure 24-2, a magnetic field is also created, because the charges flowing in the antenna constitute an electric current, which produces a magnetic field. Figure 24-3 illustrates the field direction at point P at the instant when the current in the antenna wire is upward. With the aid of Right-Hand Rule No. 2 (thumb of right hand points along the current I, fingers curl in the direction of ), the magnetic field at P can be seen to point into the page. As the oscillating current changes, the magnetic field changes accordingly. The magnetic fields created at earlier times propagate outward as a wave, just as the electric fields do.

Figure 24-3 The oscillating current I in the antenna wires creates a magnetic field at point P that is tangent to a circle centered on the wires. The field is directed as shown when the current is upward and is directed in the opposite direction when the current is downward.

Notice that the magnetic field in Figure 24-3 is perpendicular to the page, whereas the electric field in Figure 24-2 lies in the plane of the page. Thus, the electric and magnetic fields created by the antenna are mutually perpendicular and remain so as they move outward. Moreover, both fields are perpendicular to the direction of travel. These perpendicular electric and magnetic fields, moving together, constitute an electromagnetic wave.
The electric and magnetic fields in Figures 24-2 and 24-3 decrease to zero rapidly with increasing distance from the antenna. Therefore, they exist mainly near the antenna and together are called the near field. Electric and magnetic fields do form a wave at large distances from the antenna, however. These fields arise from an effect that is different from that which produces the near field and are referred to as the radiation field. Faraday’s law of induction provides part of the basis for the radiation field. As Section 22.4 discusses, this law describes the emf or potential difference produced by a changing magnetic field. And, as Section 19.4 explains, a potential difference can be related to an electric field. Thus, a changing magnetic field produces an electric field. Maxwell predicted that the reverse effect also occurs—namely, that a changing electric field produces a magnetic field. The radiation field arises because the changing magnetic field creates an electric field that fluctuates in time and the changing electric field creates the magnetic field.
Figure 24-4 shows the electromagnetic wave of the radiation field far from the antenna. The picture shows only the part of the wave traveling along the axis. The parts traveling in the other directions have been omitted for clarity. It should be clear from the drawing that an electromagnetic wave is a transverse wave because the electric and magnetic fields are both perpendicular to the direction in which the wave travels. Moreover, an electromagnetic wave, unlike a wave on a string or a sound wave, does not require a medium in which to propagate. Electromagnetic waves can travel through a vacuum or a material substance, since electric and magnetic fields can exist in either one.

Figure 24-4 This picture shows the wave of the radiation field far from the antenna. Observe that and are perpendicular to each other, and both are perpendicular to the direction of travel.

Electromagnetic waves can be produced in situations that do not involve a wire antenna. In general, any electric charge that is accelerating emits an electromagnetic wave, whether the charge is inside a wire or not. In an alternating current, an electron oscillates in simple harmonic motion along the length of the wire and is one example of an accelerating charge.
All electromagnetic waves move through a vacuum at the same speed, and the symbol c is used to denote its value. This speed is called the speed of light in a vacuum and is . In air, electromagnetic waves travel at nearly the same speed as they do in a vacuum, but, in general, they move through a substance such as glass at a speed that is substantially less than c.
The frequency of an electromagnetic wave is determined by the oscillation frequency of the electric charges at the source of the wave. In Figures 24-2, 24-3 and 24-4 the wave frequency would equal the frequency of the ac generator. Suppose, for example, that the antenna is broadcasting electromagnetic waves known as radio waves. The frequencies of AM radio waves lie between 545 and 1605 kHz, these numbers corresponding to the limits of the AM broadcast band on the radio dial. The frequencies of FM radio waves lie between 88 and 108 MHz on the dial. Television channels 2–6, on the other hand, utilize electromagnetic waves with frequencies between 54 and 88 MHz, and channels 7–13 use frequencies between 174 and 216 MHz.
Radio and television reception involves a process that is the reverse of that outlined earlier for the creation of electromagnetic waves. When broadcasted waves reach a receiving antenna, they interact with the electric charges in the antenna wires. Either the electric field or the magnetic field of the waves can be used. To take full advantage of the electric field, the wires of the receiving antenna must be parallel to the electric field, as Figure 24-5 indicates. The electric field acts on the electrons in the wire, forcing them to oscillate back and forth along the length of the wire. Consequently, an ac current exists in the antenna and the circuit connected to it. The variable-capacitor and the inductor L in the circuit provide one way to select the frequency of the desired electromagnetic wave. By adjusting the value of the capacitance, it is possible to adjust the corresponding resonant frequency of the circuit [, Equation 23.10] to match the frequency of the wave. Under the condition of resonance, there will be a maximum oscillating current in the inductor. Because of mutual inductance, this current creates a maximum voltage in the second coil in the drawing, and this voltage can then be amplified and processed by the remaining radio or television circuitry.

Figure 24-5 A radio wave can be detected with a receiving antenna wire that is parallel to the electric field of the wave. The magnetic field of the radio wave has been omitted for simplicity.

The physics of radio and television reception.

To detect the magnetic field of a broadcasted radio wave, a receiving antenna in the form of a loop can be used, as Figure 24-6 shows. For best reception, the normal to the plane of the wire loop is oriented parallel to the magnetic field. Then, as the wave sweeps by, the magnetic field penetrates the loop, and the changing magnetic flux induces a voltage and a current in the loop, in accord with Faraday’s law. Once again, the resonant frequency of a capacitor/inductor combination can be adjusted to match the frequency of the desired electromagnetic wave. Both straight wire and loop antennas can be seen on the ship in Figure 24-7.

Figure 24-6 With a receiving antenna in the form of a loop, the magnetic field of a broadcasted radio wave can be detected. The normal to the plane of the loop should be parallel to the magnetic field for best reception. For clarity, the electric field of the radio wave has been omitted.

Figure 24-7 This cruise ship uses both straight and loop antennas to communicate with other vessels and on-shore stations. (Harvey Lloyd)

The physics of cochlear implants.

Cochlear implants use the broadcasting and receiving of radio waves to provide assistance to hearing-impaired people who have auditory nerves that are at least partially intact. These implants utilize radio waves to bypass the damaged part of the hearing mechanism and access the auditory nerve directly, as Figure 24-8 illustrates. An external microphone (often set into an ear mold) detects sound waves and sends a corresponding electrical signal to a speech processor small enough to be carried in a pocket. The speech processor encodes these signals into a radio wave, which is broadcast from an external transmitter coil placed over the site of a miniature receiver (and its receiving antenna) that has been surgically inserted beneath the skin. The receiver acts much like a radio. It detects the broadcasted wave and from the encoded audio information produces electrical signals that represent the sound wave. These signals are sent along a wire to electrodes that are implanted in the cochlea of the inner ear. The electrodes stimulate the auditory nerves that feed directly between structures within the cochlea and the brain. To the extent that the nerves are intact, a person can learn to recognize sounds.

Figure 24-8 Hearing-impaired people can sometimes recover part of their hearing with the help of a cochlear implant. Broadcasting and receiving electromagnetic waves play central roles in this device.

The broadcasting and receiving of radio waves is also now being used in the practice of endoscopy. In this medical diagnostic technique a device called an endoscope is used to peer inside the body. For example, to examine the interior of the colon for signs of cancer, a conventional endoscope (known as a colonoscope) is inserted through the rectum. (See Section 26.3.) The wireless capsule endoscope shown in Figure 24-9 bypasses this invasive procedure completely. With a size of about , this capsule can be swallowed and carried through the gastrointestinal tract by the involuntary contractions of the walls of the intestines (peristalsis). The capsule is self-contained and uses no external wires. A marvel of miniaturization, it contains a radio transmitter and its associated antenna, batteries, a white-light-emitting diode (see Section 23.5) for illumination, and an optical system to capture the digital images. As the capsule moves through the intestine, the transmitter broadcasts the images to an array of small receiving antennas attached to the patient’s body. These receiving antennas also are used to determine the position of the capsule within the body. The radio waves that are used lie in the ultrahigh-frequency, or UHF, band, from to Hz.

Figure 24-9 This wireless capsule endoscope is designed to be swallowed. As it passes through a patient’s intestines, it broadcasts video images of the interior of the intestines. (Courtesy Given Imaging, Ltd.)

The physics of wireless capsule endoscopy.

Radio waves are only one part of the broad spectrum of electromagnetic waves that has been discovered. The next section discusses the entire spectrum.

Four views of the Crab Nebula, which is the remnant of a star that underwent a supernova explosion in 1054 AD. It is located 6300 light-years away from the earth. Each view is in a different region of the electromagnetic spectrum, as indicated. [(a) Courtesy NASA; (b) Mount Stromlo and Siding Spring Observatories/Photo Researchers; (c) photo by Ken Chambers of UH/IFA—photo provided courtesy of Keck Observatory; (d) NRAO/AUI/NSF/Science Photo Library/Photo Researchers.]

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.