9.3: Producing Electromagnetic Radiation
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- 472627
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Learning Objectives
- Describe the electric and magnetic waves as they move out from a source, such as an AC generator.
- Describe the characterstics of how blackbody radiation works.
We can get a good understanding of electromagnetic waves (EM) by considering how they are produced. Whenever a current varies, associated electric and magnetic fields vary, moving out from the source like waves. Perhaps the easiest situation to visualize is a varying current in a long straight wire, produced by an AC generator at its center, as illustrated in Figure \(\PageIndex{1}\).
The electric field (\(\mathbf{E}\)) shown surrounding the wire is produced by the charge distribution on the wire. Both the \(\mathbf{E}\) and the charge distribution vary as the current changes. The changing field propagates outward at the speed of light.
There is an associated magnetic field (\(\mathbf{B}\)) which propagates outward as well (see Figure \(\PageIndex{2}\)). The electric and magnetic fields are closely related and propagate as an electromagnetic wave. This is what happens in broadcast antennae such as those in radio and TV stations.
Closer examination of the one complete cycle shown in Figure \(\PageIndex{1}\) reveals the periodic nature of the generator-driven charges oscillating up and down in the antenna and the electric field produced. At time \(t=0\), there is the maximum separation of charge, with negative charges at the top and positive charges at the bottom, producing the maximum magnitude of the electric field (or \(E\)-field) in the upward direction. One-fourth of a cycle later, there is no charge separation and the field next to the antenna is zero, while the maximum \(E\)-field has moved away at speed \(c\).
As the process continues, the charge separation reverses and the field reaches its maximum downward value, returns to zero, and rises to its maximum upward value at the end of one complete cycle. The outgoing wave has an amplitude proportional to the maximum separation of charge. Its wavelength (\(\lambda\)) is proportional to the period of the oscillation and, hence, is smaller for short periods or high frequencies. (As usual, wavelength and frequency (\(f\)) are inversely proportional.)
Electric and Magnetic Waves: Moving Together
Based on Maxwell's equations, current in the antenna produces a magnetic field, as shown in Figure
The magnetic field lines also propagate away from the antenna at the speed of light, forming the other part of the electromagnetic wave, as seen in Figure \(\PageIndex{2}\)(b). The magnetic part of the wave has the same period and wavelength as the electric part, since they are both produced by the same movement and separation of charges in the antenna.
The electric and magnetic waves are shown together at one instant in time in Figure \(\PageIndex{3}\). The electric and magnetic fields produced by a long straight wire antenna are exactly in phase. Note that they are perpendicular to one another and to the direction of propagation, making this a transverse wave.
Electromagnetic waves generally propagate out from a source in all directions, sometimes forming a complex radiation pattern. A linear antenna like this one will not radiate parallel to its length, for example. The wave is shown in one direction from the antenna in Figure \(\PageIndex{3}\) to illustrate its basic characteristics.
Instead of the AC generator, the antenna can also be driven by an AC circuit. In fact, charges radiate whenever they are accelerated. But while a current in a circuit needs a complete path, an antenna has a varying charge distribution forming a standing wave, driven by the AC. The dimensions of the antenna are critical for determining the frequency of the radiated electromagnetic waves. This is a resonant phenomenon and when we tune radios or TV, we vary electrical properties to achieve appropriate resonant conditions in the antenna.
Receiving Electromagnetic Waves
Electromagnetic waves carry energy away from their source, similar to a sound wave carrying energy away from a standing wave on a guitar string. An antenna for receiving EM signals works in reverse. And like antennas that produce EM waves, receiver antennas are specially designed to resonate at particular frequencies.
An incoming electromagnetic wave accelerates electrons in the antenna, setting up a standing wave. If the radio or TV is switched on, electrical components pick up and amplify the signal formed by the accelerating electrons. The signal is then converted to audio and/or video format. Sometimes big receiver dishes are used to focus the signal onto an antenna.
In fact, charges radiate whenever they are accelerated. When designing circuits, we often assume that energy does not quickly escape AC circuits, and mostly this is true. A broadcast antenna is specially designed to enhance the rate of electromagnetic radiation, and shielding is necessary to keep the radiation close to zero. Some familiar phenomena are based on the production of electromagnetic waves by varying currents. Your microwave oven, for example, sends electromagnetic waves, called microwaves, from a concealed antenna that has an oscillating current imposed on it.
Producing Electromagnetic Radiation
There are many ways in which electromagnetic radiation can be produced. The device which Hertz created was just one artificial method that produced a very low energy electromagnetic wave. Other processes with much higher frequencies and energies are produced in nature. One of the most important processes is related to how we receive most of our light: high temperature objects radiating energy as discussed previously in this text. (Though this is not the only way of emitting light, more efficient fluorescent and light emitting diode technologies now allow us to only emit the wavelengths of light that are useful for illumination.)
For processes which radiate electromagnetic energy as a function of temperature, something called a blackbody is a useful model for first approximations. A blackbody is a convenient, ideal emitter that approximates the behavior of many materials when heated. It is “ideal” in the sense that it ignores more complicated interactions in order to simplify the math. A good approximation of a blackbody that can be used to observe blackbody radiation is a metal oven that can be heated to very high temperatures. The oven has a small hole allowing for the light being emitted within the oven to be observed with a spectrometer so that the wavelengths and their intensities can be measured. Both the Sun and the tungsten filament from a standard light bulb emit light according to the characteristics of blackbody radiation. If a blackbody is heated, we will first see it begin to glow a red color, and as it increases in temperature it might move though orange into yellow into white. The color we see is a combination of colors of various intensities being emitted from the blackbody, as shown in Figure \(\PageIndex{4}\). Notice that even though the light emitted exists along a spectrum, there is a maximum intensity that is associated with the temperature at which the radiation occurs. We can know the different wavelengths at which light is emitted by using devices to create a spectrograph which separate the light. We will discuss the methods necessary to create a spectrograph later in the chapter.
If a glowing object is observed to have a color other than red, orange, yellow, or white, it is not a blackbody but emitting light in a different way which we will discuss later in this text. (There are some extraterrestrial exceptions to this, but it requires temperatures above 7000 K, hotter than the Sun, and definitely hotter than anything we encounter on the Earth.)
Figure \(\PageIndex{4}\): Blackbody spectral distribution curves are shown for some representative temperatures.
Section Summary
- Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation.
- Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
- Blackbody radiation is a model for electromagnetic radiation emitted from objects based on their absolute temperature, and follows characteristic patterns.
Glossary
- electric field
- a vector quantity (E); the lines of electric force per unit charge, moving radially outward from a positive charge and in toward a negative charge
- electric field strength
- the magnitude of the electric field, denoted E-field
- magnetic field
- a vector quantity (B); can be used to determine the magnetic force on a moving charged particle
- magnetic field strength
- the magnitude of the magnetic field, denoted B-field
- transverse wave
- a wave, such as an electromagnetic wave, which oscillates perpendicular to the axis along the line of travel
- standing wave
- a wave that oscillates in place, with nodes where no motion happens
- wavelength
- the distance from one peak to the next in a wave
- amplitude
- the height, or magnitude, of an electromagnetic wave
- frequency
- the number of complete wave cycles (up-down-up) passing a given point within one second (cycles/second)
- resonant
- a system that displays enhanced oscillation when subjected to a periodic disturbance of the same frequency as its natural frequency
- oscillate
- to fluctuate back and forth in a steady beat
- blackbody
- a convenient, ideal emitter that approximates the behavior of many materials when heated.