ELECTRICITY

the phenomenon associated with stationary or moving electric charges. Electric charge is a fundamental property of matter and is borne by elementary particles. In electricity the particle involved is the electron, which carries a charge designated, by convention, as negative. Thus, the various manifestations of electricity are the result of the accumulation or motion of numbers of electrons. Among the earliest electrical phenomena to be studied were those produced by stationary charges, or static electricity. The Greeks discovered that amber, rubbed with fur, attracted light objects such as feathers, and the word electric comes from the Greek elektron, meaning amber. Serious study of electricity did not begin until the end of the 16th century, when William Gilbert investigated the relation of static electricity and magnetism. Benjamin Franklin proved the electrical nature of lightning in 1752 in his famous kite experiment, and he established the conventional use of negative and positive to distinguish kinds of charge. By the middle of the 18th century, two broad classes of electrical materials had been recognized: insulators, which acquired and retained a static positive or negative surface electric charge when rubbed, and conductors, mostly metals, which did not acquire a charge by rubbing but which were able to carry away the charge from an insulator. It was also found that a conducting body could store a charge if it was insulated from its surroundings. (The acquisition of surface charge by an insulator is now attributed to the ability of atoms either to lose an outer electron, and so exhibit a net positive charge, or to gain an outer electron for a net negative charge.) In 1767 Joseph Priestley established that electric charges attract with a force inversely proportional to distance, just as Newton had found gravity to do. The science of electrostatics was polished by Henry Cavendish, Charles-Augustin de Coulomb, and Simon-Denis Poisson. At the beginning of the 19th century, Count Alessandro Volta invented the electric pile, or battery, which was soon developed by others into a practical source of electric current. Within 20 years electric current and static electricity were shown to be manifestations of the same phenomenon. Sir Humphry Davy isolated the metal potassium in 1807 by passing an electric current through an electrolyte of fused potash; from these beginnings sprang electroplating, electrolytic refining, and other operations of the electrochemical industry. In 1808 Davy demonstrated that electricity could provide light or heat when he separated two charcoal electrodes that were carrying a current and drew an arc. In 1820 Hans Christian rsted observed the deflection of a compass needle when a nearby conductor carried an electric current and deduced that the current produced its own magnetic field in the space around the conductor. In 1831 Michael Faraday demonstrated the inverse action, whereby a magnetic field induces an electromotive force in a moving conductor. This discovery led to the development of the dynamo, the electric motor, and the transformer. The crowning achievement of 19th-century science was the set of field equations published by James Clerk Maxwell in 1864 that united electrical, magnetic, and optical phenomena in a single universal force, electromagnetism. The application of what was once a laboratory curiosity to industry and everyday life began in earnest in the latter half of the 19th century. It was not until 1873 that Zenobe Thophile Gramme demonstrated that electric power could be transmitted efficiently from place to place by overhead conductors. After the invention of the incandescent lamp by Thomas A. Edison in 1879 and his construction of the first central power station and distribution system in New York City in 1881, electric power began to be introduced rapidly into the factory and the home. Electricity had by that time already been applied to communication in the form of the electric telegraph and the telephone. The discovery of the electron by J.J. Thomson in the 1890s, followed quickly by the invention of the diode in 1904 and the triode in 1907, may be taken as marking the historical transition of the science of electricity into the science of electronics (q.v.). phenomenon associated with stationary or moving electric charges. Electric charge is a fundamental property of matter and is borne by elementary particles. In electricity the particle involved is the electron, which carries a charge designated, by convention, as negative. Thus, the various manifestations of electricity are the result of the accumulation or motion of numbers of electrons. Additional reading P.C.W. Davies, The Forces of Nature, 2nd ed. (1986), is an interesting, readable account. Donald M. Trotter, Jr., Capacitors, Scientific American, 259(1):8690B (July 1988), provides insight into capacitor functions and their role in technology. David N. Schramm and Gary Steigman, Particle Accelerators Test Cosmological Theory, Scientific American, 258(6):6672 (June 1988), discusses the fundamental constituents of nature. Edward M. Purcell, Electricity and Magnetism, 2nd ed. (1985), is superbly illustrated and treats key principles and phenomena with remarkable insight. Many examples and problems on electricity, as well as elementary discussions of vectors and other aspects of physics, are found in David Halliday and Robert Resnick, Fundamentals of Physics, 3rd ed. (1988). Useful physics textbooks with illustrations, examples, and problems include Richard Wolfson and Jay M. Pasachoff, Physics (1987); and Francis W. Sears, Mark W. Zemansky,and Hugh D. Young, University Physics, 7th ed. (1987). Harald A. Enge, Introduction to Nuclear Physics (1966), provides an overview of the electric properties of matter. Robert Eisberg and Robert Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. (1985), broadly treats quantum mechanical effects in various phenomena, including electric properties such as conduction in solids. Reference books include Reference Data for Engineers: Radio, Electronics, Computer, and Communications, 7th ed. (1985), with data and discussion about electric properties of matter; and CRC Handbook of Chemistry and Physics (annual), an indispensable handbook. Edwin Kashy Sharon Bertsch McGrayne Direct electric current Basic phenomena and principles Many electric phenomena occur under what is termed steady-state conditions. This means that such electric quantities as current, voltage, and charge distributions are not affected by the passage of time. For instance, because the current through a filament inside a car headlight does not change with time, the brightness of the headlight remains constant. An example of a nonsteady-state situation is the flow of charge between two conductors that are connected by a thin conducting wire and that initially have an equal but opposite charge. As current flows from the positively charged conductor to the negatively charged one, the charges on both conductors decrease with time, as does the potential difference between the conductors. The current therefore also decreases with time and eventually ceases when the conductors are discharged. In an electric circuit under steady-state conditions, the flow of charge does not change with time and the charge distribution stays the same. Since charge flows from one location to another, there must be some mechanism to keep the charge distribution constant. In turn, the values of the electric potentials remain unaltered with time. Any device capable of keeping the potentials of electrodes unchanged as charge flows from one electrode to another is called a source of electromotive force, or simply an emf. Figure 12: Motion of charge in electric current i (see text). Figure 12 shows a wire made of a conducting material such as copper. By some external means, an electric field is established inside the wire in a direction along its length. The electrons that are free to move will gain some speed. Since they have a negative charge, they move in the direction opposite that of the electric field. The current i is defined to have a positive value in the direction of flow of positive charges. If the moving charges that constitute the current i in a wire are electrons, the current is a positive number when it is in a direction opposite to the motion of the negatively charged electrons. (If the direction of motion of the electrons were also chosen to be the direction of a current, the current would have a negative value.) The current is the amount of charge crossing a plane transverse to the wire per unit timei.e., in a period of one second. If there are n free particles of charge q per unit volume with average velocity v and the cross-sectional area of the wire is A, the current i, in elementary calculus notation, is where dQ is the amount of charge that crosses the plane in a time interval dt. The unit of current is the ampere (A); one ampere equals one coulomb per second. A useful quantity related to the flow of charge is current density, the flow of current per unit area. Symbolized by J, it has a magnitude of i/A and is measured in amperes per square metre. Wires of different materials have different current densities for a given value of the electric field E; for many materials, the current density is directly proportional to the electric field. This behaviour is represented by Ohm's law: The proportionality constant sJ is the conductivity of the material. In a metallic conductor, the charge carriers are electrons and, under the influence of an external electric field, they acquire some average drift velocity in the direction opposite the field. In conductors of this variety, the drift velocity is limited by collisions, which heat the conductor. Figure 12: Motion of charge in electric current i (see text). If the wire in Figure 12 has a length l and area A and if an electric potential difference of V is maintained between the ends of the wire, a current i will flow in the wire. The electric field E in the wire has a magnitude V/l. The equation for the current, using Ohm's law, is or The quantity l/sJA, which depends on both the shape and material of the wire, is called the resistance R of the wire. Resistance is measured in ohms (W). The equation for resistance, is often written as where r is the resistivity of the material and is simply 1/sJ. The geometric aspects of resistance in equation (20) are easy to appreciate: the longer the wire, the greater the resistance to the flow of charge. A greater cross-sectional area results in a smaller resistance to the flow. The resistive strain gauge is an important application of equation (20). Strain, dl/l, is the fractional change in the length of a body under stress, where dl is the change of length and l is the length. The strain gauge consists of a thin wire or narrow strip of a metallic conductor such as constantan, an alloy of nickel and copper. A strain changes the resistance because the length, area, and resistivity of the conductor change. In constantan, the fractional change in resistance dR/R is directly proportional to the strain with a proportionality constant of approximately 2. A common form of Ohm's law is where V is the potential difference in volts between the two ends of an element with an electric resistance of R ohms and where i is the current through that element. Table 2 lists the resistivities of certain materials at room temperature. These values depend to some extent on temperature; therefore, in applications where the temperature is very different from room temperature, the proper values of resistivities must be used to calculate the resistance. As an example, equation (20) shows that a copper wire 59 metres long and with a cross-sectional area of one square millimetre has an electric resistance of one ohm at room temperature. Conductors, insulators, and semiconductors Materials are classified as conductors, insulators, or semiconductors according to their electric conductivity. The classifications can be understood in atomic terms. Electrons in an atom can have only certain well-defined energies, and, depending on their energies, the electrons are said to occupy particular energy levels. In a typical atom with many electrons, the lower energy levels are filled, each with the number of electrons allowed by a quantum mechanical rule known as the Pauli exclusion principle. Depending on the element, the highest energy level to have electrons may or may not be completely full. If two atoms of some element are brought close enough together so that they interact, the two-atom system has two closely spaced levels for each level of the single atom. If 10 atoms interact, the 10-atom system will have a cluster of 10 levels corresponding to each single level of an individual atom. In a solid, the number of atoms and hence the number of levels is extremely large; most of the higher energy levels overlap in a continuous fashion except for certain energies in which there are no levels at all. Energy regions with levels are called energy bands, and regions that have no levels are referred to as band gaps. The highest energy band occupied by electrons is the valence band. In a conductor, the valence band is partially filled, and since there are numerous empty levels, the electrons are free to move under the influence of an electric field; thus, in a metal the valence band is also the conduction band. In an insulator, electrons completely fill the valence band; and the gap between it and the next band, which is the conduction band, is large. The electrons cannot move under the influence of an electric field unless they are given enough energy to cross the large energy gap to the conduction band. In a semiconductor, the gap to the conduction band is smaller than in an insulator. At room temperature, the valence band is almost completely filled. A few electrons are missing from the valence band because they have acquired enough thermal energy to cross the band gap to the conduction band; as a result, they can move under the influence of an external electric field. The holes left behind in the valence band are mobile charge carriers but behave like positive charge carriers. For many materials, including metals, resistance to the flow of charge tends to increase with temperature. For example, an increase of 5 C (9 F) increases the resistivity of copper by 2 percent. In contrast, the resistivity of insulators and especially of semiconductors such as silicon and germanium decreases rapidly with temperature; the increased thermal energy causes some of the electrons to populate levels in the conduction band where, influenced by an external electric field, they are free to move. The energy difference between the valence levels and the conduction band has a strong influence on the conductivity of these materials, with a smaller gap resulting in higher conduction at lower temperatures. Figure 12: Motion of charge in electric current i (see text). The values of electric resistivities listed in Table 2 show an extremely large variation in the capability of different materials to conduct electricity. The principal reason for the large variation is the wide range in the availability and mobility of charge carriers within the materials. The copper wire in Figure 12, for example, has many extremely mobile carriers; each copper atom has approximately one free electron, which is highly mobile because of its small mass. An electrolyte, such as a saltwater solution, is not as good a conductor as copper. The sodium and chlorine ions in the solution provide the charge carriers. The large mass of each sodium and chlorine ion increases as other attracted ions cluster around them. As a result, the sodium and chlorine ions are far more difficult to move than the free electrons in copper. Pure water also is a conductor, although it is a poor one because only a very small fraction of the water molecules are dissociated into ions. The oxygen, nitrogen, and argon gases that make up the atmosphere are somewhat conductive because a few charge carriers form when the gases are ionized by radiation from radioactive elements on the Earth as well as from extraterrestrial cosmic rays (i.e., high-speed atomic nuclei and electrons). Electrophoresis is an interesting application based on the mobility of particles suspended in an electrolytic solution. Different particles (proteins, for example) move in the same electric field at different speeds; the difference in speed can be utilized to separate the contents of the suspension. A current flowing through a wire heats it. This familiar phenomenon occurs in the heating coils of an electric range or in the hot tungsten filament of an electric light bulb. This ohmic heating is the basis for the fuses used to protect electric circuits and prevent fires; if the current exceeds a certain value, a fuse, which is made of an alloy with a low melting point, melts and interrupts the flow of current. The power P dissipated in a resistance R through which current i flows is given by where P is in watts (one watt equals one joule per second), i is in amperes, and R is in ohms. According to Ohm's law, the potential difference V between the two ends of the resistor is given by V = iR, and so the power P can be expressed equivalently as In certain materials, however, the power dissipation that manifests itself as heat suddenly disappears if the conductor is cooled to a very low temperature. The disappearance of all resistance is a phenomenon known as superconductivity. As mentioned earlier, electrons acquire some average drift velocity v under the influence of an electric field in a wire. Normally the electrons, subjected to a force because of an electric field, accelerate and progressively acquire greater speed. Their velocity is, however, limited in a wire because they lose some of their acquired energy to the wire in collisions with other electrons and in collisions with atoms in the wire. The lost energy is either transferred to other electrons, which later radiate, or the wire becomes excited with tiny mechanical vibrations referred to as phonons. Both processes heat the material. The term phonon emphasizes the relationship of these vibrations to another mechanical vibrationnamely, sound. In a superconductor, a complex quantum mechanical effect prevents these small losses of energy to the medium. The effect involves interactions between electrons and also those between electrons and the rest of the material. It can be visualized by considering the coupling of the electrons in pairs with opposite momenta; the motion of the paired electrons is such that no energy is given up to the medium in inelastic collisions or phonon excitations. One can imagine that an electron about to collide with and lose energy to the medium could end up instead colliding with its partner so that they exchange momentum without imparting any to the medium. A superconducting material widely used in the construction of electromagnets is an alloy of niobium and titanium. This material must be cooled to a few degrees above absolute zero temperature, -263.66 C (or 9.5 K), in order to exhibit the superconducting property. Such cooling requires the use of liquefied helium, which is rather costly. During the late 1980s, materials that exhibit superconducting properties at much higher temperatures were discovered. These temperatures are higher than the -196 C of liquid nitrogen, making it possible to use the latter instead of liquid helium. Since liquid nitrogen is plentiful and cheap, such materials may provide great benefits in a wide variety of applications, ranging from electric power transmission to high-speed computing. Electric properties of matter Piezoelectricity Some solids, notably certain crystals, have permanent electric polarization. Other crystals become electrically polarized when subjected to stress. In electric polarization, the centre of positive charge within an atom, molecule, or crystal lattice element is separated slightly from the centre of negative charge. Piezoelectricity (literally pressure electricity) is observed if a stress is applied to a solid, for example, by bending, twisting, or squeezing it. If a thin slice of quartz is compressed between two electrodes, a potential difference occurs; conversely, if the quartz crystal is inserted into an electric field, the resulting stress changes its dimensions. Piezoelectricity is responsible for the great precision of clocks and watches equipped with quartz oscillators. It also is used in electric guitars and various other musical instruments to transform mechanical vibrations into corresponding electric signals, which are then amplified and converted to sound by acoustical speakers. A crystal under stress exhibits the direct piezoelectric effect; a polarization P, proportional to the stress, is produced. In the converse effect, an applied electric field produces a distortion of the crystal, represented by a strain proportional to the applied field. The basic equations of piezoelectricity are P = d stress and E = strain/d. The piezoelectric coefficient d (in metres per volt) is approximately 3 10-12 for quartz, 5 -10-11 for ammonium dihydrogen phosphate, and 3 10-10 for lead zirconate titanate. For an elastic body, the stress is proportional to the straini.e., stress = Ye strain. The proportionality constant is the coefficient of elasticity Ye, also called Young's modulus for the English physicist Thomas Young. Using that relation, the induced polarization can be written as P = dYe strain, while the stress required to keep the strain constant when the crystal is in an electric field is stress = -dYeE. The strain in a deformed elastic body is the fractional change in the dimensions of the body in various directions; the stress is the internal pressure along the various directions. Both are second-rank tensors, and, since electric field and polarization are vectors, the detailed treatment of piezoelectricity is complex. The equations above are oversimplified but can be used for crystals in certain orientations. The polarization effects responsible for piezoelectricity arise from small displacements of ions in the crystal lattice. Such an effect is not found in crystals with a centre of symmetry. The direct effect can be quite strong; a potential V = Yedd/e0K is generated in a crystal compressed by an amount d, where K is the dielectric constant. If lead zirconate titanate is placed between two electrodes and a pressure causing a reduction of only 1/20th of one millimetre is applied, a 100,000-volt potential is produced. The direct effect is used, for example, to generate an electric spark with which to ignite natural gas in a heating unit or an outdoor cooking grill. In practice, the converse piezoelectric effect, which occurs when an external electric field changes the dimensions of a crystal, is small because the electric fields that can be generated in a laboratory are minuscule compared to those existing naturally in matter. A static electric field of 106 volts per metre produces a change of only about 0.001 millimetre in the length of a one-centimetre quartz crystal. The effect can be enhanced by the application of an alternating electric field of the same frequency as the natural mechanical vibration frequency of the crystal. Many of the crystals have a quality factor Q of several hundred, and, in the case of quartz, the value can be 106. The result is a piezoelectric coefficient a factor Q higher than for a static electric field. The very large Q of quartz is exploited in electronic oscillator circuits to make remarkably accurate timepieces. The mechanical vibrations that can be induced in a crystal by the converse piezoelectric effect are also used to generate ultrasound, which is sound with a frequency far higher than frequencies audible to the human earabove 20 kilohertz. The reflected sound is detectable by the direct effect. Such effects form the basis of ultrasound systems used to fathom the depths of lakes and waterways and to locate fish. Ultrasound has found application in medical imaging (e.g., fetal monitoring and the detection of abnormalities such as prostate tumours). The use of ultrasound makes it possible to produce detailed pictures of organs and other internal structures because of the variation in the reflection of sound from various body tissues. Thin films of polymeric plastic with a piezoelectric coefficient of about 10 -11 metres per volt are being developed and have numerous potential applications as pressure transducers. Electro-optic phenomena The index of refraction n of a transparent substance is related to its electric polarizability and is given by n2 = 1 + ce/e0. As discussed earlier, ce is the electric susceptibility of a medium, and the equation P = ceE relates the polarization of the medium to the applied electric field. For most matter, ce is not a constant independent of the value of the electric field, but rather depends to a small degree on the value of the field. Thus, the index of refraction can be changed by applying an external electric field to a medium. In liquids, glasses, and crystals that have a centre of symmetry, the change is usually very small. Called the Kerr effect (for its discoverer, the Scottish physicist John Kerr), it is proportional to the square of the applied electric field. In noncentrosymmetric crystals, the change in the index of refraction n is generally much greater; it depends linearly on the applied electric field and is known as the Pockels effect (after the German physicist F. R. Pockels). A varying electric field applied to a medium will modulate its index of refraction. This change in the index of refraction can be used to modulate light and make it carry information. A crystal widely used for its Pockels effect is potassium dihydrogen phosphate, which has good optical properties and low dielectric losses even at microwave frequencies. An unusually large Kerr effect is found in nitrobenzene, a liquid with highly acentric molecules that have large electric dipole moments. Applying an external electric field partially aligns the otherwise randomly oriented dipole moments and greatly enhances the influence of the field on the index of refraction. The length of the path of light through nitrobenzene can be adjusted easily because it is a liquid.