60 Production of Electromagnetic Waves

Electromagnetic (EM) waves are produced whenever electric charges accelerate. A changing electric current creates changing electric and magnetic fields, which propagate away from their source through space as waves. This process is responsible for many technologies used in everyday life and healthcare, including radio and television broadcasting, Wi-Fi communication, magnetic resonance imaging (MRI), and wireless medical monitoring devices.

One of the simplest ways to visualize the generation of an electromagnetic wave is to consider a long straight wire connected to an alternating-current (AC) generator, as shown in Figure 60.1. As the generator reverses direction, electric charges in the wire move back and forth. This oscillating motion creates electric and magnetic fields that continually change with time and propagate outward at the speed of light.

The electric field, represented by the vector [latex]\mathbf{E}[/latex], is produced by the separation of positive and negative charges along the antenna. As the current changes, the amount of charge separation also changes, causing the electric field to grow, shrink, and reverse direction. These changes do not remain confined to the antenna. Instead, they travel outward through space as part of an electromagnetic wave.

A changing electric field is always accompanied by a changing magnetic field, represented by [latex]\mathbf{B}[/latex]. As we will see in Figure 60.2, these two fields are inseparable—they are generated together and propagate together. This is the same physical principle that allows broadcast antennas to transmit radio and television signals, MRI systems to generate radio-frequency pulses, and wireless medical devices to communicate without direct electrical connections.

Examining one complete cycle of the antenna's motion illustrates how the wave is generated. At time
[latex]t=0[/latex], the separation of positive and negative charges is greatest, producing the strongest upward electric field. One-quarter of a cycle later, the charges are evenly distributed and the electric field at the antenna becomes zero, while the previously generated electric field continues traveling away from the antenna at the speed of light,
[latex]c[/latex].

During the next half-cycle, the charge separation reverses, producing an electric field in the opposite direction. By the end of one complete cycle, the antenna has returned to its original state, while a complete electromagnetic wave has propagated outward.

The size of the emitted wave depends on the maximum separation of charge in the antenna, which determines the wave's amplitude. The distance between successive peaks is the wavelength, denoted by [latex]\lambda[/latex]. Because the wave travels at the speed of light, its wavelength depends on the oscillation frequency:

This relationship shows that higher-frequency electromagnetic waves have shorter wavelengths, while lower-frequency waves have longer wavelengths. For example, radio waves used for communication have wavelengths ranging from meters to kilometers, whereas visible light has wavelengths of only a few hundred nanometers, and X-rays used in medical imaging have even shorter wavelengths.

Electric and Magnetic Waves: Moving Together

Whenever electric charges move, they produce a magnetic field. According to Ampère's law, the alternating current flowing in the antenna generates a magnetic field that forms concentric circles around the wire, as shown in Figure 60.2. Because the current continually changes direction and magnitude, the magnetic field also changes with time.

Just as the changing electric field travels outward from the antenna, the changing magnetic field also propagates through space at the speed of light. Together, these two fields form a single electromagnetic wave. Because both fields originate from the same oscillating charges, they have the same frequency, the same wavelength, and remain synchronized as they travel.

The relationship between the electric and magnetic fields is illustrated in Figure 60.3. The electric field ([latex]\mathbf{E}[/latex]) and magnetic field ([latex]\mathbf{B}[/latex]) reach their maximum and minimum values at the same time—they are said to be in phase. Furthermore, each field is perpendicular to the other, and both are perpendicular to the direction in which the wave travels.

Because the oscillations occur at right angles to the direction the wave travels, electromagnetic waves are classified as transverse waves. This is similar to the motion of a wave traveling along a stretched rope, where the rope moves up and down while the disturbance travels horizontally. In an electromagnetic wave, however, nothing material is oscillating. Instead, the electric and magnetic fields themselves vary as the wave moves through space.

Although Figure 60.3 shows the wave traveling in a single direction for simplicity, a real antenna usually radiates electromagnetic energy in many directions. The exact radiation pattern depends on the antenna's shape and dimensions. For example, a straight dipole antenna radiates very little energy along its own axis but emits strongly in directions perpendicular to the antenna.

In practice, antennas are driven by alternating-current circuits that cause charges to accelerate back and forth. Accelerating charges always emit electromagnetic radiation. The length of an antenna is carefully chosen so that it resonates with the desired wavelength, making the transmission or reception of electromagnetic waves much more efficient. The same principle is used in radio and television broadcasting, cellular communications, Wi-Fi routers, MRI systems, and many wireless medical monitoring devices.

Receiving Electromagnetic Waves

Electromagnetic waves carry energy away from their source, just as sound waves carry energy away from a vibrating guitar string. However, unlike sound waves, electromagnetic waves can travel through empty space without requiring a material medium. An antenna designed to receive electromagnetic waves operates in the opposite way from a transmitting antenna. Just as transmitting antennas are built to efficiently emit radiation at specific frequencies, receiving antennas are designed to resonate most strongly with particular frequencies.

When an electromagnetic wave reaches a receiving antenna, its oscillating electric field exerts forces on the free electrons in the metal conductor. These electrons accelerate back and forth at the same frequency as the incoming wave, producing an alternating current in the antenna. If the receiver is tuned to the correct resonant frequency, the electrical signal is greatly enhanced and can be processed by the electronic circuitry.

In a radio receiver, this tiny alternating electrical signal is amplified and converted into sound by a speaker. In a television, smartphone, or Wi-Fi receiver, the electrical signal is decoded into audio, video, or digital information. Satellite communication systems often use large parabolic dishes to collect electromagnetic waves over a wide area and focus them onto a much smaller receiving antenna, increasing the strength of the detected signal.

The ability of antennas to transmit and receive electromagnetic waves is based on the same fundamental principle: accelerating electric charges emit electromagnetic radiation, and electromagnetic waves, in turn, accelerate charges in conductors. Maxwell's theory predicts both processes, making transmission and reception two complementary aspects of the same phenomenon.

In most electrical circuits, electromagnetic radiation is undesirable because it represents energy escaping from the circuit. Engineers therefore use shielding, grounded enclosures, and carefully designed wiring to minimize unintended radiation. In contrast, communication devices intentionally maximize radiation by using antennas whose dimensions are chosen to efficiently emit or receive waves at specific wavelengths.

Many everyday technologies rely on this principle. Radio and television broadcasting, cellular networks, Wi-Fi, Bluetooth devices, satellite communications, and GPS all transmit information using electromagnetic waves. Microwave ovens also generate electromagnetic waves—specifically microwaves—that are produced by oscillating electric currents inside a device called a magnetron. These microwaves are directed into the cooking chamber, where they are absorbed primarily by water molecules in food, causing them to rotate rapidly and produce thermal energy that heats the food.

Relating Electric and Magnetic Field Strengths

The electric field and magnetic field in an electromagnetic wave are not independent of one another. Instead, their magnitudes are directly related. This relationship can be understood by considering the transmitting antenna discussed earlier. A larger separation of charge in the antenna produces a stronger electric field. That stronger electric field is associated with a larger oscillating current, which in turn generates a stronger magnetic field.

Because the current is proportional to the applied voltage (through Ohm's law), and the voltage is proportional to the electric field strength, the electric and magnetic fields increase and decrease together. Maxwell's equations show that their ratio is always equal to the speed of light:

where:

• [latex]E[/latex] is the magnitude of the electric field (V/m),
• [latex]B[/latex] is the magnitude of the magnetic field (T), and
• [latex]c=3.00\times10^8\ \text{m/s}[/latex] is the speed of light in a vacuum.

This elegant relationship is true everywhere in an electromagnetic wave and at every instant in time. Whenever the electric field reaches its maximum value, the magnetic field also reaches its maximum value. As the wave propagates, both fields remain in phase while maintaining the constant ratio given above.

This result is also consistent with Maxwell's prediction that changing electric fields produce magnetic fields. Although the magnetic fields generated by changing electric fields are often quite small, they become measurable through resonance. Heinrich Hertz exploited this principle in his famous experiments by building receiving circuits whose natural frequency matched that of the incoming electromagnetic waves. Modern radio receivers, televisions, MRI scanners, Wi-Fi devices, and cellular phones all use the same basic idea: they selectively resonate with electromagnetic waves of the desired frequency while rejecting signals at other frequencies.

Interactive Exploration: Radio Waves and Electromagnetic Fields

Radio waves are electromagnetic waves produced by accelerating electric charges. In this simulation, you will investigate how an oscillating electron generates changing electric and magnetic fields that propagate through space as electromagnetic waves. You will also observe how these waves transfer energy from a transmitting antenna to a receiving antenna without any physical connection between them.

Experiment by moving the transmitting electron manually or allowing it to oscillate automatically. Switch between the vector and wave representations of the fields, and use the strip chart to compare the motion of the transmitting and receiving electrons. As you explore, connect your observations to the concepts of electromagnetic wave generation, propagation, and wireless communication discussed in this chapter.

Conceptual Questions

1. The direction of the electric field shown in each part of Figure 60.1 is determined by the distribution of positive and negative charge along the antenna. Use Coulomb's law and the definition of the electric field,
   [latex]\mathbf{E}=\mathbf{F}/q[/latex], where [latex]q[/latex] is a positive test charge, to explain why the electric field points in the direction shown at each stage of the oscillation.
2. Is the direction of the magnetic field shown in Figure 60.2(a) consistent with the right-hand rule for the direction of the current? Explain your reasoning.
3. Why is the direction of the current shown in each part of Figure 60.2 opposite to the direction of the electric field produced by the charge separation on the antenna?
4. In which situation shown in Figure 60.5 will the electromagnetic wave be more effective at inducing a current in the straight wire? Explain your answer.

5. In which situation shown in Figure 60.6 will the electromagnetic wave be more effective at inducing a current in the wire loop? Explain your reasoning.

6. A radio station broadcasts using a vertical transmitting antenna.
   1. Should a straight receiving antenna be oriented vertically or horizontally for the strongest reception? Explain.
   2. How should a loop antenna be oriented to best receive the signal?
   3. Why can the preferred orientation of a loop antenna be used to determine the direction of the transmitter, such as when tracking radio-tagged wildlife?
7. Under what conditions could wires carrying direct current (DC) emit electromagnetic waves?
8. Give one example of interference between electromagnetic waves in everyday life or technology.
9. Figure 60.7 shows the interference pattern produced by two radio antennas broadcasting the same signal.
   1. Explain how this pattern is analogous to the interference produced by two loudspeakers emitting the same sound.
   2. Could this principle be used to create a directional antenna system that broadcasts more strongly in certain directions than in others? Explain.

10. Can a transmitting or receiving antenna have any arbitrary length? Explain why the physical dimensions of an antenna are important for efficient transmission and reception of electromagnetic waves.