EM Fields Help (page 3)
Isaac Newton believed that visible light is composed of tiny particles, or corpuscles . Today we recognize these particles as photons. However, light is more complex than can be represented by the particle theory. It has wave-like characteristics too. The same is true of all forms of radiant energy.
The wave nature of radiant energy is the result of interaction of electricity and magnetism. Charged particles, such as electrons and protons, are surrounded by electrical fields . Magnetic poles or moving charged particles produce magnetic fields . When the fields are strong enough, they extend a considerable distance. When electrical and magnetic fields vary in intensity, we have an electromagnetic (EM) field .
You have observed the attraction between opposite poles of magnets and the repulsion between like poles. Similar effects occur with electrically charged objects. These forces seem to operate only over short distances under laboratory conditions, but this is so because such fields weaken rapidly, as the distance between poles increases to less than the smallest intensity we can detect. In theory, the fields extend into space indefinitely.
A constant electric current in a wire produces a magnetic field around the wire. The lines of magnetic flux are perpendicular to the direction of the current. The existence of a constant voltage difference between two nearby objects produces an electrical field; the lines of electrical flux are parallel to the gradient of the charge differential. When the intensity of a current or voltage changes with time, things get more interesting.
A fluctuating current in a wire or a variable charge gradient between two nearby objects gives rise to a magnetic field and an electrical field in combination. These fields leapfrog through space so that the EM field can travel long distances with less attenuation than either an electrical field or a magnetic field alone. The electrical and magnetic fields in such a situation are perpendicular to each other everywhere in space. The direction of travel of the resulting EM field is perpendicular to both the electrical and magnetic lines of flux, as shown in Fig. 18-1.
In order for an EM field to exist, the electrons in a wire or other conductor not only must be set in motion, but they also must be accelerated. That is, their velocity must be made to change. The most common method of creating this sort of situation is the introduction of an alternating current (ac) in an electrical conductor. It also can result from the bending of charged-particle beams by electrical or magnetic fields.
Frequency And Wavelength
EM waves travel through space at the speed of light, which is approximately 2.99792 × 10 8 m/s (1.86262 × 10 5 mi/s). This is often rounded up to 3.00 × 10 8 m/s, expressed to three significant figures. The wavelength of an EM field in free space gets shorter as the frequency becomes higher. At 1 kHz, the wavelength is about 300 km. At 1 MHz, the wavelength is about 300 m. At 1 GHz, the wavelength is about 300 mm. At 1 THz, an EM signal has a wavelength of 0.3 mm—so small that you would need a magnifying glass to see it.
The frequency of an EM wave can get much higher than 1 THz; some of the most energetic known rays have wavelengths of 0.00001 Ångström (10 −5 Å). The Ångström is equivalent to 10 −10 m and is used by some scientists to denote extremely short EM wavelengths. A microscope of great magnifying power would be needed to see an object with a length of 1 Å. Another unit, increasingly preferred by scientists these days, is the nanometer (nm), where 1 nm = 10 −9 m = 10 Å.
The formula for wavelength λ, in meters, as a function of the frequency f , in hertz, for an EM field in free space is
λ = 2.99792 × 10 8 / f
This same formula can be used for λ in millimeters and f in kilohertz, for λ in micrometers and f in megahertz, and for λ in nanometers and f in gigahertz. Remember your prefix multipliers: 1 millimeter (1 mm) is 10 −3 m, 1 micrometer (1 μm) is 10 −6 m, and 1 nanometer (1 nm) is 10 −9 m.
The formula for frequency f , in hertz, as a function of the wavelength λ, in meters, for an EM field in free space is given by transposing f and λ in the preceding formula:
f = 2.99792 × 10 8 /λ
As in the preceding case, this formula will work for f in kilohertz and λ in millimeters, for f in megahertz and λ in micrometers, and for f in gigahertz and λ in nanometers.
The discovery of EM fields led ultimately to the variety of wireless communications systems we know today. Radio waves are not the only form of EM radiation. As the frequency increases above that of conventional radio, we encounter new forms. First comes microwaves . Then comes infrared (IR) or “heat rays.” After that comes visible light, ultraviolet (UV) radiation, x-rays, and gamma (γ) rays.
In the opposite, and less commonly imagined, sense, EM fields can exist at frequencies far below those of radio signals. In theory, an EM wave can go through one complete cycle every hour, day, year, thousand years, or million years. Some astronomers suspect that stars and galaxies generate EM fields with periods of years, centuries, or millennia.
The Em Wavelength Scale
To illustrate the range of EM wavelengths, we use a logarithmic scale. The logarithmic scale is needed because the range is so great that a linear scale is impractical. The left-hand portion of Fig. 18-2 is such a logarithmic scale that shows wavelengths from 10 8 m down to 10 −12 m. Each division, in the direction of shorter wavelength, represents a 100-fold decrease, or two orders of magnitude. Utility ac is near the top of this scale; the wavelength of 60-Hz ac in free space is quite long. The gamma rays are denoted approximately at the bottom; their EM wavelengths are tiny. It is apparent here that visible light takes up only a tiny sliver of the EM spectrum . In the right-hand scale, visible wavelengths are denoted in nanometers (nm).
Fig. 18-2 . The EM spectrum from wavelengths of 10 8 m down to 10 −12 m, and an exploded view of the visible-light spectrum within.
How Little We See!
To get some idea of what a small EM “window” is represented by the visible-light wavelengths, try looking through a red- or blue-colored piece of glass or cellophane. Such a color filter greatly restricts the view you get of the world because only a narrow range of visible wavelengths can pass through it. Different colors cannot be ascertained through the filter. For example, when a scene is viewed through a red filter, everything is a shade of red or nearly red. Blue appears the same as black, bright red appears the same as white, and maroon red appears the same as gray. Other colors look red with varying degrees of saturation, but there is little or no variation in the hue. If our eyes had built-in red color filters, we would be pretty much color-blind.
When considered with respect to the entire EM spectrum, all optical instruments suffer from the same sort of handicap we would have if the lenses in our eyeballs were tinted red. The range of wavelengths we can detect with our eyes is approximately 770 nm at the longest and 390 nm at the shortest. Energy at the longest visible wavelengths appears red to our eyes, and energy at the shortest visible wavelengths appears violet. The intervening wavelengths show up as orange, yellow, green, blue, and indigo.
EM Fields Practice Problems
What is the frequency of a red laser beam whose waves measure 7400 Å?
Use the formula for frequency in terms of wavelength. Note that 7400 Å = 7400 × 10 −10 m = 7.400 × 10 −7 m. Then the frequency in hertz is found as follows:
f = 2.99792 × 10 8 /λ
= 2.99792 × 10 8 /(7.400 × 10 −7 )
= 4.051 × 10 14 Hz
This is 405.1 THz. To give you an idea of how high this frequency is, compare it with a typical frequency-modulated (FM) broadcast signal at 100 MHz. The frequency of the red light beam is more than 4 million times as high.
What is the wavelength of the EM field produced in free space by the ac in a common utility line? Take the frequency as 60.0000 Hz (accurate to six significant figures).
Use the formula for wavelength in terms of frequency:
λ = 2.99792 × 10 8 /f
= 2.99792 × 10 8 /60.0000
= 4.99653 × 10 6 m
This is about 5,000 km, or half the distance from the Earth’s equator to the north geographic pole as measured over the surface of the globe.
Practice problems of these concepts can be found at: Forms of Radiation Practice Test
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