Electromagnetic Fields Help (page 3)

Electromagnetic Fields

The optical telescope was invented long before scientists knew that visible light represents only a tiny part of a continuum of energy wavelengths. Isaac Newton believed that visible light was composed of tiny particles or corpuscles . Today we recognize these particles as photons . However, light is more complex than can be represented by the simple corpuscular theory . The same is true of all forms of radiant energy.

The wave nature of visible light, and of other forms of radiant energy, is the result of synergistic interaction of electrical and magnetic forces. Charged particles, such as electrons and protons, are surrounded by electrical (E) fields . Magnetic poles produce magnetic (M) fields . The fields extend into the space surrounding the charged particles or magnetic poles, and when the fields are strong enough, their effects can be noticed at a considerable distance. When the E and M fields vary in intensity, the result is an electromagnetic (EM) field .

Orderly, well-defined EM fields are generated by voltages or currents that vary in a rhythmic way. Conversely, an EM field can give rise to alternating voltages or currents. These effects can occur over vast distances in space.

Static E And M Fields

If you’ve ever played with permanent magnets, you have noticed the attraction between opposite poles and the repulsion between like poles. Similar effects take place with electrically charged objects. These forces seem to operate only over short distances under laboratory conditions. This is so because static (steady, unchanging) E and M 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.

Physicists have known for a long time that a constant electric current in a wire produces an M field around the wire. The lines of magnetic flux are perpendicular to the direction of the current. It is also known that the existence of a constant voltage difference between two nearby objects produces an E field; the lines of electrical flux are parallel to the direction in which the voltage varies most rapidly with distance. When the intensity of a current or voltage changes with time, things get more interesting.

Fluctuating Fields

A fluctuating current in a wire or a variable voltage between two nearby objects gives rise to both an M field and an E field. These fields regenerate each other, so they can travel for long distances with less attenuation than either type of field all by itself. The E and M lines of flux in such a situation are perpendicular to each other everywhere in space. The direction of travel of the attendant EM field is perpendicular to both the E and M lines of flux, as shown in Fig. 18-1.

Figure 18-1. An EM wave is comprised of fluctuating, mutually perpendicular electric and magnetic lines of flux. The field travels perpendicular to both sets of flux lines.

In order for an EM field to exist, electrons or other charge carriers not only must be moving, but also must be accelerating. That is, their velocity must be constantly changing. 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 E or M fields.

Frequency and Wavelength

Frequency

The frequency of an EM field can be very low, such as a few cycles per second, or hertz (abbreviated Hz), and can range upward into the thousands, millions, billions, or trillions of hertz. A frequency of 1,000 Hz is a kilohertz (kHz); a frequency of 1,000 kHz is a megahertz (MHz); a frequency of 1,000 MHz is a gigahertz (GHz); and a frequency of 1,000 GHz is a terahertz (THz).

Wavelength

Electromagnetic waves travel through space at the speed of light, which is approximately 2.99792 × 10 ⁸ m/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 0.300 m or 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 the waves, if they were in fact directly visible.

The frequency of an EM wave can get much higher than 1 THz; some of the most energetic rays known have wavelengths of 0.000001 nanometer (10 ^–6 nm). The nanometer equivalent to 10 ^–9 m and is used commonly by scientists to measure the wavelengths of EM disturbances at visible wavelengths and shorter. A microscope of great magnifying power would be needed to see an object with a length of 1 nm. Less commonly, the Ångström (Å) is used to denote extremely short wavelengths. This unit is 1/10 of a nanometer; that is, 1 Å = 10 ^–10 m = 0.1 nm.

Many Forms

The discovery of EM fields led to the “wireless” radio and ultimately to the sophisticated and complex variety of 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 come the microwaves . Then comes infrared (IR), or “heat rays.” After that comes visible light, ultraviolet (UV) radiation, x-ray energy, and gamma-ray energy.

In the opposite, and less commonly imagined, sense, EM fields can exist at frequencies far below those of radio signals. Some extremely-low-frequency (ELF) fields have frequencies less than the 50 or 60 Hz of ac utility electricity. 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 Spectrum

The wavelengths of the lowest-frequency EM fields can extend, at least theoretically, for light-years. The shortest gamma rays have, as we have already mentioned, wavelengths that measure only a tiny fraction of a nanometer. In between these extremes lie all the forms of EM energy.

The Em Wavelength Scale

To illustrate the range of EM wavelengths, scientists often use a logarithmic scale. It is necessary to use a logarithmic scale 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 and shows wavelengths from 10 ⁸ down to 10 ^–12 m. Each division, in the direction of shorter wavelength, represents a tenfold decrease, known as a mathematical order of magnitude (not to be confused with star magnitude). Utility ac is near the top of this scale; the wavelength of 60-Hz ac in free space is quite long. Gamma rays are at the bottom; their EM wavelengths are tiny.

Figure 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.

From this example, it is easy to see that visible light takes up only a tiny sliver of the EM spectrum. However, this diagram makes the visible portion of the realm look much larger than it is in linear proportion. If the scale were linear in this illustration, the visible slice would be thinner than the diameter of an atom. Along the right-hand scale, visible wavelengths are denoted in nanometers.

How Little We See!

The next time you get a chance, look 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, blue appears the same as black, and crimson appears the same as gray or white. 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, our view of the world would be much different; we would essentially be 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 wavelength appears red to our eyes, and energy at the shortest visible wavelength appears violet. The intervening wavelengths show up as orange, yellow, green, blue, and indigo.

In order to “see” EM energy waves above and below the visible spectrum, we need special apparatus. Astronomers have devised an amazing variety of instruments that can detect energy all the way from the radio spectrum through microwaves, IR, visible, UV, x-rays, and even gamma rays.

Atmospheric Em Transparency

The observation of the Universe at the visible wavelengths is not greatly hindered by the atmosphere of Earth. Some diffusion and refraction take place, but the air is essentially transparent at the range of 770 to 390 nm. At some other wavelengths, however, energy from outer space can’t make it to the ground, so we can’t detect it unless we put instruments high up in the atmosphere or in outer space.

At radio wavelengths greater than a few meters, Earth’s ionosphere , at altitudes ranging from about 60 km (40 mi) to 400 km (250 mi), causes absorption, refraction, and reflection of EM waves. This keeps signals from space away from us at certain radio frequencies. This same effect keeps shortwave radio waves near the Earth and makes long-distance communication possible.

At UV wavelengths, the ozone in the air is highly absorptive. In the x-ray and gamma-ray parts of the EM spectrum, our atmosphere completely obscures our view of the heavens. However, some portions of the invisible spectrum are observable with ground-based equipment, especially the wavelengths between microwaves and visible light.

One of the most significant developments in the exploration of space at invisible wavelengths has been the radio telescope. Radio astronomy has become a refined science since the development of wireless communications equipment and in particular since the end of World War II in the 1940s. High-altitude rockets, orbiting satellites, and the advent of the space age have opened up the realms of UV, x-ray, and gamma-ray astronomy.

Radar Astronomy—The Moon and Venus

The huge parabolic antennas used in some radio telescopes, as well as other forms of high-gain antenna systems, can work for transmitting in the same way as they function for receiving. The large power gain developed in the interception of a faint signal from space also can increase the effective transmitted power of a signal greatly. By sending out short pulses of radio energy, generated by a transmitter in the laboratory, and then listening for possible echoes, astronomers can make accurate determinations of the distances to other objects in the Solar System. The use of radio telescopes for distance determination, motion analysis, and surface mapping of extraterrestrial objects is called radar astronomy .

The Moon And Venus

The distance to Earth’s Moon has been refined to within a few centimeters, and it is possible to tell how fast the Moon is moving toward or away from Earth as it revolves around our planet. The surface of the Moon has been mapped by radar, and the quality of detail rivals that of optical photographs. Radar astronomy has proven to be a valuable tool in the study of the surface of Venus because that planet’s thick clouds make it impossible to see the surface with optical apparatus.

The main challenge to pursuing radar investigations of the planets has been the development of radar sets with enough power and sensitivity. The planets are very distant in terms of human-made radio transmissions. In addition, they do not reflect radio signals the way a mirror reflects visible light. Only a minuscule part of the rf signal reaching a planet is reflected back in the general direction of the Earth; of this reflected wave, only a tiny portion ever gets back to the antenna. Radar technology eventually was perfected to overcome the path loss between Earth and Venus. The radar telescope enabled scientists to discover that Venus has a retrograde motion on its axis. Before that time, astronomers had made educated guesses concerning the planet’s rotation based on the motion of the cloud tops, and these guesses had all been wrong.

Radar mapping of the surface of Venus was attempted because rf signals easily penetrate the visually opaque clouds. Astronomers found that the surface is solid but irregular. High-resolution maps were obtained when the planet was scrutinized using radar sets aboard Venus-orbiting spacecraft. The solidity of the surface was not known with certainty until it was verified by radar.

Mercury

Observations of Mercury have been made by radar. Surface details of Mercury are difficult to resolve with optical telescopes based on the Earth’s surface because that planet is always near the Sun in the sky. The rotation rate of Mercury was once believed to be 88 Earth days, identical with its period of revolution around the Sun. The radar telescope revealed that one rotation is completed in 59 Earth days. Mercury has a day of its own, but it is long and strange by our standards.

Echoes from the planet Mercury have been used to verify one of the predictions of Albert Einstein’s general theory of relativity. According to Einstein’s equations, radio waves passing close to a massive object, such as the Sun, should appear to “slow down” because of the curvature of space in the gravitational field. All radiant energy, according to general relativity, is affected in this way near massive celestial objects.

Experimenters bounced radar signals off Mercury as it passed on the far side of the Sun (Fig. 18-5). According to general relativity, an illusion should occur in which Mercury seems to deviate about 65 km outside its orbital path as it passes behind the Sun. This deviation was found, and it takes place to the exact extent predicted by Einstein. The echoes are slightly delayed as the signals pass near the Sun on their way to and from Mercury.

Figure 18-5. Mercury appears to deviate outside its orbit when it passes behind the Sun. (The extent of the deviation is exaggerated in this drawing.)

Meteor Orbits

Radar astronomy is useful in the study of meteors. Meteors apparently come, for the most part, from inside the Solar System; they are not interstellar wanderers. This can be deduced by determining the velocities of large numbers of meteors relative to Earth. The velocities of meteors as they enter the atmosphere can be measured accurately using radar. Such measurements are difficult or impossible to do by visual means. From the radar information, an astronomer can figure out the original paths of meteors through space. These paths always turn out to be orbits around the Sun.

Meteors arrive during the day as well as at night, and the radar telescope can “see” them in visual daylight as well as in visual darkness. This gives the radar-equipped observer another advantage over the visual observer.

The Sun In Uv

The Sun’s surface temperature is in the neighborhood of 6,000°C (11,000°F). Our parent star emits some UV, but not a great deal of it as stars go. This is fortunate for the kind of life that has evolved on this planet. If the Sun were a hotter star, life on any Earthlike planet in its system would have developed in a different way, if at all.

The Sun’s UV radiation has been investigated using equipment aboard rockets and satellites. The UV surface of the Sun is somewhat above the visual surface. This tells us that as the altitude above the photosphere (visible surface) increases the temperature rises. If our eyes suddenly became responsive to a range of wavelengths only half as long as they actually are—say, a continuum of 200 to 400 nm—the disk of the Sun would seem a little larger than it appears in the visible range. We would ascribe to the Sun a different photosphere.

If our eyes suddenly became UV eyes, the Sun not only would look slightly larger in size but it also would appear less bright. The atmosphere of Earth transmits EM rays poorly in the short-wavelength part of the range 200 to 400 nm. Assuming that the longest detectable wavelengths appeared “red” to us, we would consider the Sun a ruddy star. Vision is a subjective thing. We would be equally impressed with the unnatural blueness and brilliance of the Sun if our eyes suddenly became responsive to, say, a wavelength range of 800 to 1,600 nm.

X-rays

The x-ray spectrum consists of EM energy at wavelengths from approximately 1 to 0.01 nm. This is 2 mathematical orders of magnitude. Proportionately, the x-ray spectrum is vast compared with the visible range.

As the wavelength of x-rays become shorter, it becomes increasingly difficult to direct and focus them. This is so because of the penetrating power of the short-wavelength rays. A piece of paper with a tiny hole can work for UV photography; in the x-ray spectrum, the radiation passes right through the paper. However, if x-rays encounter a reflecting surface at a nearly grazing angle, and if the reflecting surface is made of suitable material, some degree of focusing can be realized. The shorter the wavelength of the EM energy, the smaller the angle relative to the surface must be if reflection is to take place. At the shortest x-ray wavelengths, the angle must be smaller than 1 degree of arc. This grazing reflection effect is shown in Fig. 18-9 A . The focusing mirror is tapered in the shape of an elongated paraboloid. Figure 18-9 B is a rough illustration of how an x-ray telescope achieves its focusing. As parallel x-rays enter the aperture of the reflector, they strike its inner surface at a grazing angle. The x-rays are brought to a focal point, where a radiation counter or detector is placed.

Figure 18-9. At A , x-rays are reflected from a surface only when they strike at a grazing angle. At B , a functional diagram of an x-ray focusing and observing device.

The resolving power of an x-ray telescope, such as the one shown in Fig. 18-9 B , is not as good as that obtainable with optical apparatus, but it does allow the observation of some celestial x-ray sources. As is the case with UV radiation, x-rays from space must be viewed from above the atmosphere of our planet; x-ray telescopes aboard rockets and satellites send their information back to Earth by radio.

Sources Of X-rays

After the development of high-altitude rockets and space vehicles, it became possible to look at the x-ray sky. Powerful x-ray sources were found, but there at first appeared to be no explanation for some of them. Even type O and B stars do not produce large amounts of radiation in the x-ray spectrum; they are not hot enough. The most interesting x-ray objects appeared to produce more energy in the x-ray region than at longer wavelengths.

Some tentative hypotheses have been brought forward to explain intense, pointlike x-ray objects, which have, because of their apparent location within our galaxy, been called x-ray stars . They are not supernovae; their radiation wavelengths are too short even for that. Besides, they are not visually bright enough to be supernovae. X-ray stars are found more commonly than supernovae. Some astronomers theorize that the x-ray objects are binary stars in very close mutual orbits. Matter from one of the stars in a binary system could be torn away from the other member by gravitational forces. The stars might even be in mutual contact. The exchange of matter between two stars in such close association could account for the production of large amounts of x-rays.

Another suggestion concerning the nature of x-ray stars has been given: They are binary star systems in which one member is a neutron star or a very dense black dwarf. Still another theory holds that the strange stars are binary systems containing black holes. The gravitational influence of a neutron star or black hole is sufficient to account for the x-rays; as matter is torn from the visible member of such a binary system, the hotter interior layers are exposed, and this can produce radiation at very short wavelengths. The idea that matter is being ripped out of a star is supported by the existence of Doppler shifts in the x-rays.

Some x-ray objects seem to be outside of our galaxy. Certain quasars and radio galaxies have been associated with strong sources of x-rays. Some astronomers have hypothesized that interaction among the photons of radiant energy at different wavelengths, as they collide with each other, could be responsible for the x-ray emissions from extragalactic objects. Some galaxies and quasars apparently have regions of tremendously high temperature—hotter than anything we know in our Milky Way—and this state of affairs can generate highly energetic EM waves that peak in the x-ray portion of the EM spectrum.

Gamma Rays

As the wavelength of EM energy becomes shorter than the hardest x-rays, it becomes more and more difficult to obtain an image. The cutoff point where the x-ray region ends and the gamma-ray region begins is approximately 0.01 nm. Gamma rays can get shorter than this without limit. The gamma classification represents the most energetic of all EM fields. Short-wavelength gamma rays can penetrate several centimeters of solid lead or more than a meter of concrete. They are even more damaging to living tissue than x-rays. Gamma rays come from radioactive materials, both natural (such as radon) and human-made (such as plutonium).

Radiation counters are the primary means of detecting and observing sources of gamma rays. Gamma rays can dislodge particles from the nuclei of atoms they strike. These subatomic particles can be detected by a counter. One type of radiation counter consists of a thin wire strung within a sealed, cylindrical metal tube filled with certain gases. When a high-speed subatomic particle enters the tube, the gas is ionized for a moment, and conduction occurs between the inner wire and the cylinder. A voltage is applied between the wire and the outer cylinder so that a pulse of current occurs whenever the gas is ionized. This pulse produces a click in the output of an amplifier connected to the device.

A simplified diagram of a radiation counter is shown in Fig. 18-10. A glass window with a metal sliding door is cut in the cylinder. The door can be opened to let in particles of lower energy and closed to allow only the fastest particles to get inside. High-speed particles, which are tiny yet massive for their size, have no trouble penetrating the window glass if they are moving fast enough. Yet gamma rays can penetrate into the tube with ease, even when the door is closed.

Cosmic Particles

If you sit in a room with no radioactive materials present and switch on a radiation counter with the window of a tube closed, you’ll notice an occasional click from the device. Some of the particles come from the Earth; there are radioactive elements in the ground almost everywhere (usually in small quantities). Some of the radiation comes indirectly from space. These particles strike atoms in the atmosphere, and these atoms in turn eject other subatomic particles that arrive at the counter tube.

Figure 18-10. Simplified diagram of a radiation counter.

The direction of arrival of high-speed atomic particles can be determined, to a certain extent, by means of a device called a cloud chamber . The air in a small enclosure can be treated especially to produce condensation when a subatomic particle enters, and the path of the particle will show up as a vapor trail.

In the early 1900s, physicists noticed radiation apparently coming from space. They found that the strange background radiation increased in intensity when observations were made at high altitude; the radiation level decreased when observations were taken from underground or underwater. This space radiation has been called secondary cosmic radiation or secondary cosmic particles . The actual particles from space, called primary cosmic particles , usually do not penetrate far into the atmosphere before they collide with and break up the nuclei of atoms. To observe primary cosmic particles, it is necessary to ascend to great heights, and as with the UV and x-ray investigations, this was not possible until the advent of the space rocket.

While the radiation in the EM spectrum—the radio waves, IR, visible light, UV, x-rays, and gamma rays—consists of photons traveling at the speed of light, cosmic particles are matter, traveling at speeds almost, but not quite, as fast as light. At such high speeds, the protons, neutrons, and other heavy particles gain mass because of relativistic effects, and this renders them almost immune to Earth’s magnetosphere. Such particles, arriving in the upper atmosphere, come to us in a nearly perfect straight-line path despite the magnetic field of our planet. By carefully observing the trails of the particles in a cloud chamber aboard a low-orbiting space ship, it is possible to ascertain the direction from which they have come. Over time, cosmic-particle maps of the heavens can be generated and compared with maps at various EM wavelengths.

Practice problems of this concept can be found at: Electromagnetic Fields Practice Problems