Chapter 24: Electromagnetic Waves PDF

Chapter 24: Electromagnetic Waves Mrs. Pooja Brahmaiahchari Introduction The beauty of a coral reef, the warm radiance of sunshine, the sting of sunburn, the X-ray revealing a broken bone, even microwave popcorn—all are brought to us by electromagnetic waves....

Chapter 24: Electromagnetic Waves Mrs. Pooja Brahmaiahchari Introduction The beauty of a coral reef, the warm radiance of sunshine, the sting of sunburn, the X-ray revealing a broken bone, even microwave popcorn—all are brought to us by electromagnetic waves. The list of the various types of electromagnetic waves, ranging from radio transmission waves to nuclear gamma-ray ( γ -ray) emissions, is interesting in itself. “Electromagnetic waves” was the name he gave to the phenomena his theory predicted by James Clerk Maxwell in mid of 19th century. MAIN THING TO KNOW, KNOW THE ORDER OF DIFFERENT WAVES BASED OFF OF THEIR WAVELENGTH AND FREQUENCY Maxwell’s Equations: Electromagnetic Waves Predicted and Observed The Scotsman James Clerk Maxwell (1831–1879) is regarded as the greatest theoretical physicist of the 19th century. Maxwell not only formulated a complete electromagnetic theory, represented by Maxwell’s equations. He also developed the kinetic theory of gases and made significant contributions to the understanding of color vision and the nature of Saturn’s rings.  Maxwell’s Equations 1. Electric field lines originate on positive charges and terminate on negative charges. The electric field is defined as the force per unit charge on a test charge, and the strength of the force is related to the electric constant 𝜀0 , also known as the permittivity of free space. From Maxwell’s first equation we obtain a special form of Coulomb’s law known as Gauss’s law for electricity. 2. Magnetic field lines are continuous, having no beginning or end. No magnetic monopoles are known to exist. The strength of the magnetic force is related to the magnetic constant 𝜇0 , also known as the permeability of free space. This second of Maxwell’s equations is known as Gauss’s law for magnetism. 3. A changing magnetic field induces an electromotive force (emf) and, hence, an electric field. The direction of the emf opposes the change. This third of Maxwell’s equations is Faraday’s law of induction and includes Lenz’s law. 4. Magnetic fields are generated by moving charges or by changing electric fields. This fourth of Maxwell’s equations encompasses Ampere’s law and adds another source of magnetism—changing electric fields.  Maxwell’s complete and symmetric theory showed that electric and magnetic forces are not separate, but different manifestations of the same thing—the electromagnetic force. This classical unification of forces is one motivation for current attempts to unify the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces. The waves predicted by Maxwell would consist of oscillating electric and magnetic fields—defined to be an electromagnetic wave (EM wave). Electromagnetic waves would be capable of exerting forces on charges great distances from their source, and they might thus be detectable.  Maxwell calculated that electromagnetic waves would propagate at a speed given by the equation 1 𝑐= 𝜇𝑜 𝜀𝑜 When the values for 𝜇𝑜 and 𝜀𝑜 are entered into the equation for c, we find that 1 𝑐= = 3 x 108 m/s −12 𝐶2 𝑇.𝑚 8.85 𝑥 10 (4𝜋 𝑥 10−7 𝐴 ) 𝑁𝑚2 which is the speed of light. In fact, Maxwell concluded that light is an electromagnetic wave having such wavelengths that it can be detected by the eye. Hertz’s Observations The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that not only confirmed the existence of electromagnetic waves, but also verified that they travel at the speed of light. Hertz used an AC (resistor-inductor-capacitor) circuit that resonates at a known 1 frequency 𝑓0 = and connected it to a loop of wire as shown in Figure. 2𝜋 𝐿𝐶  High voltages induced across the gap in the loop produced sparks that were visible evidence of the current in the circuit and that helped generate electromagnetic waves. Hertz had another loop attached to another RLC circuit, which could be tuned (as the dial on a radio) to the same resonant frequency as the first and could, thus, be made to receive electromagnetic waves. This loop also had a gap across which sparks were generated, giving solid evidence that electromagnetic waves had been received. Hertz also studied the reflection, refraction, and interference patterns of the electromagnetic waves he generated, verifying their wave character. The SI unit for frequency, the hertz is named in his honor. Production of Electromagnetic Waves 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.  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 is proportional to the period of the oscillation and, hence, is smaller for short periods or high frequencies.  The electric field ( E) shown surrounding the wire is produced by the charge distribution on the wire. Both the 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 (B ) which propagates outward as well (see Figure). 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. Electric and Magnetic Waves: Moving Together Following Ampere’s law, current in the antenna produces a magnetic field, as shown in figure below. The relationship between E and B is shown at one instant is shown. (a) The current in the antenna produces the circular magnetic field lines. The current (I) produces the separation of charge along the wire, which in turn creates the electric field as shown. (b) The electric and magnetic fields (E and B) near the wire are perpendicular; they are shown here for one point in space. (c) The magnetic field varies with current and propagates away from the antenna at the speed of light.  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.  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. An incoming electromagnetic wave accelerates electrons in the antenna, setting up a standing wave. Sometimes big receiver dishes are used to focus the signal onto an antenna. The 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. Relating E-Field and B-Field Strengths The stronger the E-field created by a separation of charge, the greater the current and, hence, the greater the B-field created. Since current is directly proportional to voltage (Ohm’s law) and voltage is directly proportional to E-field strength, the two should be directly proportional. It can be shown that the magnitudes of the fields do have a constant ratio, equal to the speed of light. That is, 𝐸 =𝑐 𝐵 1. What is the maximum strength of B-Field in an electromagnetic wave that has maximum E-Field strength of 1000 V/m? 2. Calculate the wavelength of A) 60Hz EM wave? B) 93.3-MHz FM radio wave, C) of a beam of visible red light from the frequency of 4.74 x 1014Hz. The Electromagnetic Spectrum As noted, an electromagnetic wave has a frequency and a wavelength associated with it and travels at the speed of light, or c. The relationship among these wave characteristics can be described by 𝑣𝑤 = 𝑓𝜆 , where 𝑣𝑤 is the propagation speed of the wave, f is the frequency, and 𝜆 is the wavelength. Here 𝑣𝑤 = c, so that for all electromagnetic waves, 𝑐 = 𝑓𝜆 Brief overview of EM waves Electromagnetic Spectrum: Rules of Thumb Three rules that apply to electromagnetic waves in general are as follows: High-frequency electromagnetic waves are more energetic and are more able to penetrate than low-frequency waves. High-frequency electromagnetic waves can carry more information per unit time than low-frequency waves. The shorter the wavelength of any electromagnetic wave probing a material, the smaller the detail it is possible to resolve. Transmission, Reflection, and Absorption What happens when an electromagnetic wave impinges on a material? If the material is transparent to the particular frequency, then the wave can largely be transmitted. If the material is opaque to the frequency, then the wave can be totally reflected. The wave can also be absorbed by the material, indicating that there is some interaction between the wave and the material, such as the thermal agitation of molecules. What is not obvious is that something that is transparent to light may be opaque at other frequencies. For example, ordinary glass is transparent to visible light but largely opaque to ultraviolet radiation. Human skin is opaque to visible light—we cannot see through people—but transparent to X-rays. Radio and TV Waves The broad category of radio waves is defined to contain any electromagnetic wave produced by currents in wires and circuits. Its name derives from their most common use as a carrier of audio information. Radio waves from outer space, for example, do not come from alien radio stations. They are created by many astronomical phenomena, and their study has revealed much about nature on the largest scales. There are many uses for radio waves, and so the category is divided into many subcategories, including microwaves and those electromagnetic waves used for AM and FM radio, cellular telephones, and TV.  The lowest commonly encountered radio frequencies are produced by high-voltage AC power transmission lines at frequencies of 50 or 60 Hz. These extremely long wavelength electromagnetic waves (about 6000 km!) are one means of energy loss in long-distance power transmission. Extremely low frequency (ELF) radio waves of about 1 kHz are used to communicate with submerged submarines. The ability of radio waves to penetrate salt water is related to their wavelength (much like ultrasound penetrating tissue)—the longer the wavelength, the farther they penetrate.  AM radio waves are used to carry commercial radio signals in the frequency range from 540 to 1600 kHz. The abbreviation AM stands for amplitude modulation, which is the method for placing information on these waves. A carrier wave having the basic frequency of the radio station, say 1530 kHz, is varied or modulated in amplitude by an audio signal. The resulting wave has a constant frequency, but a varying amplitude.  A radio receiver tuned to have the same resonant frequency as the carrier wave can pick up the signal, while rejecting the many other frequencies impinging on its antenna. The receiver’s circuitry is designed to respond to variations in amplitude of the carrier wave to replicate the original audio signal. That audio signal is amplified to drive a speaker or perhaps to be recorded. Amplitude modulation for AM radio. (a) A carrier wave at the station’s basic frequency. (b) An audio signal at much lower audible frequencies. (c) The amplitude of the carrier is modulated by the audio signal without changing its basic frequency. FM Radio Waves FM radio waves are also used for commercial radio transmission, but in the frequency range of 88 to 108 MHz. FM stands for frequency modulation, another method of carrying information. Carrier wave having the basic frequency of the radio station, perhaps 105.1 MHz, is modulated in frequency by the audio signal. FM radio is inherently less subject to noise from stray radio sources than AM radio. The reason is that amplitudes of waves add. So an AM receiver would interpret noise added onto the amplitude of its carrier wave as part of the information.  Television is also broadcast on electromagnetic waves. Since the waves must carry a great deal of visual as well as audio information, each channel requires a larger range of frequencies than simple radio transmission. TV channels utilize frequencies in the range of 54 to 88 MHz and 174 to 222 MHz. These TV channels are called VHF (for very high frequency). Other channels called UHF (for ultra high frequency) utilize an even higher frequency range of 470 to 1000 MHz. The TV video signal is AM, while the TV audio is FM. Satellite dishes and cable transmission of TV occurs at significantly higher frequencies and is rapidly evolving with the use of the high-definition or HD format. Radio Wave Interference Astronomers and astrophysicists collect signals from outer space using electromagnetic waves. A common problem for astrophysicists is the “pollution” from electromagnetic radiation pervading our surroundings from communication systems in general. Even everyday gadgets like our car keys and TV remotes involve radio-wave frequencies. The reason sometimes we are asked to switch off our mobile phones in airplanes and in hospitals is that important communications or medical equipment often uses similar radio frequencies, and their operation can be affected by frequencies used in the communication devices. Ex: MRI scan  MRI is an important medical imaging and research tool, producing highly detailed two- and three-dimensional images. Radio waves are broadcast, absorbed, and reemitted in a resonance process that is sensitive to the density of nuclei. The wavelength of 100-MHz radio waves is 3 m, yet using the sensitivity of the resonant frequency to the magnetic field strength, details smaller than a millimeter can be imaged. The intensity of the radio waves used in MRI presents little or no hazard to human health. Microwaves They have high frequencies; their wavelengths are short compared with those of other radio waves—hence the name “microwave.” Microwaves can also be produced by atoms and molecules. They are, for example, a component of electromagnetic radiation generated by thermal agitation. The thermal motion of atoms and molecules in any object at a temperature above absolute zero causes them to emit and absorb radiation. Since it is possible to carry more information per unit time on high frequencies, microwaves are quite suitable for communications.  Most satellite-transmitted information is carried on microwaves, as are land-based long-distance transmissions. A clear line of sight between transmitter and receiver is needed because of the short wavelengths involved. Radar is a common application of microwaves that was first developed in World War II. By detecting and timing microwave echoes, radar systems can determine the distance to objects as diverse as clouds and aircraft. A Doppler shift in the radar echo can be used to determine the speed of a car or the intensity of a rainstorm. Sophisticated radar systems are used to map the Earth and other planets, with a resolution limited by wavelength. Heating with Microwaves Water and some other constituents of food have a slightly negative charge at one end and a slightly positive charge at one end (called polar molecules). The range of microwave frequencies is specially selected so that the polar molecules, in trying to keep orienting themselves with the electric field, absorb these energies and increase their temperatures—called dielectric heating. The energy thereby absorbed results in thermal agitation heating food and not the plate, which does not contain water. Hot spots in the food are related to constructive and destructive interference patterns. Rotating antennas and food turntables help spread out the hot spots.  Another use of microwaves for heating is within the human body. Microwaves will penetrate more than shorter wavelengths into tissue and so can accomplish “deep heating”. This is used for treating muscular pains, spasms, tendonitis, and rheumatoid arthritis. Microwaves generated by atoms and molecules far away in time and space can be received and detected by electronic circuits. Deep space acts like a blackbody with a 2.7 K temperature, radiating most of its energy in the microwave frequency range. Infrared Radiation The microwave and infrared regions of the electromagnetic spectrum overlap. Infrared radiation is generally produced by thermal motion and the vibration and rotation of atoms and molecules. Electronic transitions in atoms and molecules can also produce infrared radiation. The range of infrared frequencies extends up to the lower limit of visible light, just below red. In fact, infrared means “below red.” Frequencies at its upper limit are too high to be produced by accelerating electrons in circuits, but small systems, such as atoms and molecules, can vibrate fast enough to produce these waves.  The Sun radiates like a nearly perfect blackbody with a 6000 K surface temperature. About half of the solar energy arriving at the Earth is in the infrared region, with most of the rest in the visible part of the spectrum, and a relatively small amount in the ultraviolet. On average, 50 percent of the incident solar energy is absorbed by the Earth. The relatively constant temperature of the Earth is a result of the energy balance between the incoming solar radiation and the energy radiated from the Earth. Visible Light Visible light is the narrow segment of the electromagnetic spectrum to which the normal human eye responds. Visible light is produced by vibrations and rotations of atoms an molecules, as well as by electronic transitions within atoms and molecules. We usually refer to visible light as having wavelengths of between 400 nm and 750 nm  Red light has the lowest frequencies and longest wavelengths, while violet has the highest frequencies and shortest wavelengths. Blackbody radiation from the Sun peaks in the visible part of the spectrum but is more intense in the red than in the violet, making the Sun yellowish in appearance. Optics is the study of the behavior of visible light and other forms of electromagnetic waves. Optics falls into two distinct categories. Ray optics is the study of such situations and includes lenses and mirrors. Physical or wave optics is the study of such situations and includes all wave characteristics. Ultraviolet Radiation Ultraviolet means “above violet.” The electromagnetic frequencies of ultraviolet radiation (UV) extend upward from violet, the highest-frequency visible light. The wavelengths of ultraviolet extend from 400 nm down to about 10 nm at its highest frequencies, which overlap with the lowest Xray frequencies. Solar UV radiation is broadly subdivided into three regions: UV-A (320– 400 nm), UV-B (290–320 nm), and UV-C (220–290 nm), ranked from long to shorter wavelengths (from smaller to larger energies). Most UV-B and all UV-C is absorbed by ozone molecules in the upper atmosphere. Consequently, 99% of the solar UV radiation reaching the Earth’s surface is UV-A. Human Exposure to UV Radiation It is largely exposure to UV-B that causes skin cancer. All UV radiation can damage collagen fibers, resulting in an acceleration of the aging process of skin and the formation of wrinkles. The tanning response is a defense mechanism in which the body produces pigments to absorb future exposures in inert skin layers above living cells. Repeated exposure to UV-B may also lead to the formation of cataracts in the eyes—a cause of blindness. A major acute effect of extreme UV exposure is the suppression of the immune system, both locally and throughout the body. UV Light and the Ozone Layer The layer of ozone (O3 ) in our upper atmosphere (10 to 50 km above the Earth) protects life by absorbing most of the dangerous UV radiation. Unfortunately, today we are observing a depletion in ozone concentrations in the upper atmosphere. This depletion has led to the formation of an “ozone hole” in the upper atmosphere. This depletion is attributed to the breakdown of ozone molecules by refrigerant gases called chlorofluorocarbons (CFCs). Benefits of UV Light Vitamin D production in the skin (epidermis) results from exposure to UVB radiation, generally from sunlight. UV radiation is used in the treatment of infantile jaundice and in some skin conditions. It is also used in sterilizing workspaces and tools, and killing germs in a wide range of applications. It is also used as an analytical tool to identify substances. When exposed to ultraviolet, some substances, such as minerals, glow in characteristic visible wavelengths, a process called fluorescence. Ultraviolet is also used in special microscopes to detect details smaller than those observable with longer-wavelength visible-light microscopes. X-Rays In the 1850s, scientists (such as Faraday) began experimenting with high- voltage electrical discharges in tubes filled with rarefied gases. It was later found that these discharges created an invisible, penetrating form of very high frequency electromagnetic radiation. This radiation was called an X-ray, because its identity and nature were unknown. There are two methods by which X-rays are created—both are submicroscopic processes and can be caused by high-voltage discharges. While the low-frequency end of the X-ray range overlaps with the ultraviolet, Xrays extend to much higher frequencies.  The widest use of X-rays is for imaging objects that are opaque to visible light, such as the human body or aircraft parts. In humans, the risk of cell damage is weighed carefully against the benefit of the diagnostic information obtained. However, questions have risen in recent years as to accidental overexposure of some people during CT scans—a mistake at least in part due to poor monitoring of radiation dose.  The ability of X-rays to penetrate matter depends on density, and so an X-ray image can reveal very detailed density information. The use of X-ray technology in medicine is called radiology—an established and relatively cheap tool in comparison to more sophisticated technologies. Consequently, X-rays are widely available and used extensively in medical diagnostics.  During World War I, mobile X-ray units, advocated by Madame Marie Curie, were used to diagnose soldiers. Because they can have wavelengths less than 0.01 nm, X-rays can be scattered (a process called X-ray diffraction) to detect the shape of molecules and the structure of crystals. X-ray diffraction was crucial to Crick, Watson, and Wilkins in the determination of the shape of the double-helix DNA molecule. X-rays are also used as a precise tool for trace-metal analysis in X-ray induced fluorescence, in which the energy of the X-ray emissions are related to the specific types of elements and amounts of materials present. Gamma Rays Soon after nuclear radioactivity was first detected in 1896, it was found that at least three distinct types of radiation were being emitted. The most penetrating nuclear radiation was called a gamma ray (γ ray) and it was later found to be an extremely high frequency electromagnetic wave. In fact, γ rays are any electromagnetic radiation emitted by a nucleus. This can be from natural nuclear decay or induced nuclear processes in nuclear reactors and weapons. The lower end of the γ ray frequency range overlaps the upper end of the X- ray range, but γ rays can have the highest frequency of any electromagnetic radiation.  Gamma rays have characteristics identical to X-rays of the same frequency—they differ only in source. At higher frequencies, γ rays are more penetrating and more damaging to living tissue. They have many of the same uses as X-rays, including cancer therapy. Gamma radiation from radioactive materials is used in nuclear medicine.  Food spoilage can be greatly inhibited by exposing it to large doses of γ radiation, thereby obliterating responsible microorganisms. Damage to food cells through irradiation occurs as well, and the long- term hazards of consuming radiation-preserved food are unknown and controversial for some groups. Both X-ray and technologies are also used in scanning luggage at airports. Detecting Electromagnetic Waves from Space The entire electromagnetic spectrum is used by researchers for investigating stars, space, and time. Penzias and Wilson detected microwaves to identify the background radiation originating from the Big Bang. Radio telescopes such as the Arecibo Radio Telescope in Puerto Rico and Parkes Observatory in Australia were designed to detect radio waves. Infrared telescopes need to have their detectors cooled by liquid nitrogen to be able to gather useful signals.  The most famous of these infrared sensitive telescopes is the James Clerk Maxwell Telescope in Hawaii. The Hubble Space Telescope (launched in 1990) gathers ultraviolet radiation as well as visible light. In the X-ray region, there is the Chandra X-ray Observatory (launched in 1999), and in the -ray region, there is the new Fermi Gamma-ray Space Telescope. Energy in Electromagnetic Waves Electromagnetic waves can bring energy into a system by virtue of their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. If the frequency of the electromagnetic wave is the same as the natural frequencies of the system, the transfer of energy is much more efficient. A wave’s energy is proportional to its amplitude squared ( E2 or B2). This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure.  In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields. Thus, the energy carried and the intensity I of an electromagnetic wave is proportional to E2 and B2. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity is given by 𝑐 𝜖0 𝐸02 𝐼𝑎𝑣𝑒 = 2 Where c is the speed of light, 𝜖0 is the permittivity of free space, and 𝐸02 is the maximum electric field strength; intensity, as always, is power per unit area.  The equation can also be represented as: 𝑐𝐵02 𝐼𝑎𝑣𝑒 = 2𝜇0 One more expression for in terms of both electric and magnetic field strengths is useful. Substituting the fact that 𝑐. 𝐸0 = 𝐵0 , the previous expression becomes 𝐸0 𝐵0 𝐼 𝑎𝑣𝑒 = 2𝜇0 Problems 1. Calculate wavelength for radio wave from a radio station that is broadcasting at 88.1 MHz. = v/f Wavlength = velocity / frequency wavelength = 3.0x10^8 / 88.1 x10^6 Wavelength = 3.4 meters = 2. Calculate frequency of red light(𝜆 = 650𝑛𝑚) frequency = velocity / wavelength frequency = 4.6 x 10^14 hz 3. A certain 50Hz AC power line radiates an Electromagnetic wave having a maximum Electric Field strength of 13.0 kV/m. a) Calculate the wavelength b) What Is the maximum magnetic field strength? E/ B = C Wavlength = velocity / frequency 13x10^3/ B = 3.0x10^8 Wavlength = 3.0x10^8 / 50 Wavlength = 6,000,000 meters B= 4.3x10^-5 T 4. What is the intensity of Electromagnetic wave with a peak electric field strength of 125V/m? 20.7 W/m^2 5. Find the intensity of EM wave having a peak magnetic field strength of 4.00 x 10-9 T? 1.91 x10 ^-3 W/m^2