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1- r Magnetic Effects 1- f 1 magnetism (MAG-ne-tizm) n.: the property associated with clmrged objects in motion, which give rise to afield of force. MAGNETISM 19.1 Magnetic Materials Physicists believe that all magnetic phenomena result from forces between electric charges in motion. Vast quantities of electric energy are now generated as a consequence of relative motion between electric conductors and magnetic fields. Electric energy is transformed into mechanical energy by relative motion between electric currents and magnetic fields. The function of many electric measuring instruments depends on the relationship between electricity and magnetism. The basic theory of electric generators and motors is presented in Chapter 20. Electric measuring instruments are discussed later in this chapter. Before undertaking the study of magnetic effects of electric currents, we shall examine the magnetic properties of substances and learn of the nature of magnetism and magnetic fields. Deposits of a magnetic iron are were discovered many centuries ago by the Greeks in a section of Turkey. The region was then known as Magnesia and the are was called magnetite. Deposits of magnetite are found in the Adirondack Mountains of New York and in other regions of the world. Pieces of magnetite are known as natural magnets. A suspended piece of magnetite aligns itself with the magnetic field of the earth. These natural magnets, known as lodestones (leading stones), were first used as magnetic compasses during the twelfth century. A few materials, notably iron and steel, are strongly attracted by magnets; cobalt and nickel are attracted to a o BJECTIVE~ . Discuss the domain theory of magnetism. . Describe the nature of the magnetic force. . Describe a magnetic monopole. Discuss the techniques for mapping magnetic fields. . Study magnetic induction. . Describe the earth's magnetic field. . Define the link between moving charges and magnetic fields of force. . . Study the magnetic field produced by the current in a straight wire and a solenoid. . Describe electric meters and their use in d-c circuits. 465 466 The Latin word for iron is "ferrum"; thus the name "ferromagnetic." Alnico (AI Ni Co) consists mainly of aluminum, nickel, and cobalt plus iron, . Figure 19-1. Iron filings attracted to a lodestone give evidence of the field of force surrounding the natural magnet. The orbiting eIeciron produces 1/ magnetic field because, in this motion, it constitutes an electric current. CHAPTER 19 lesser degree. These substances are said to have ferromagnetic properties. Special alloys such as permalloy and alnico have extraordinary ferromagnetic properties. Physicists have shown much interest in the structure of materials possessing the property of ferromagnetism. Today very strong magnets are made from ferromagnetic substances. Alnico magnets may support a weight of over 1000 times that of the magnets themselves. Ferromagnetic substances are commonly referred to simply as "magnetic substances." Materials are commonly classified as magnetic or nonmagnetic. Those that do not demonstrate the strong ferromagnetism of the Iron Family of metals are said to be "nonmagnetic." However, if these materials are placed in the field of a very strong magnet, some are observed to be slightly repelled by the magnet while others are very slightly attracted. Zinc, bismuth, sodium chloride, gold, and mercury are a few of the substances that are feebly repelled; they are diamagnetic. The property of diamagnetism is an important concept in the modern theory of magnetism, as we shall see in Section 19.2. Wood, aluminum, platinum, oxygen, and copper(IJ) sulfate are examples of substances that are very slightly attracted by a strong magnet. Such materials are paramagnetic, and this magnetic behavior is called paramagnetism. 19.2 The Domain Theory of Magnetism William Gilbert's report on his experiments with natural magnets, published in 1600, probably represents the first scientific study of magnetism. In the years that followed, discoveries by Coulomb, Oersted, and Ampere added to our knowledge of the behavior of magnets and the nature of magnetic forces. Physicists believe, however, that it is only within this century that they have begun to understand the true nature of magnetism. The present view is that the magnetic properties of matter are electric in origin and result from the movements of electrons within the atoms of substances. Since the electron is an electrically charged particle, this theory suggests that magnetism is a property of a charge in motion. If so, we can account for the energy associated with magnetic forces by using known laws of physics. Two kinds of electron motion are important in this modern concept of magnetism. First, an electron revolvingabout the nucleus of an atom imparts a magnetic property to the atom structure. See Figure 19-2. When the atoms of a substance are subjected to the magnetic force of a strong magnet, the r' MAGNETIC 467 EFFECTS force affects this magnetic property, opposing the motion of the electrons. The atoms are thus repelled by the magnet. This is diamagnetism. If the electron's only motion were its movement about the nucleus, all substances would be diamagnetic. Diamagnetic repulsion is quite feeble in its action on the total mass of a substance. The second kind of motion is that of the electron spinning on its own axis. Each spinning electron acts asa tiny permanentmagnet. Opposite spins are designated as + and - spins; electrons spinning in opposite directions tend to form pairs and so neutralize their magnetic character. See Figure 19-3. The magnetic character of an atom as a whole may be weak because of the mutual interaction between the electron spins. Figure 19-2. Revolving electrons impart a magnetic property to the atom. , , Figure 19-3. Ferromagnetism in matter from the spin of electrons. Magnetic properties are associated with both kinds of electron motion. The atoms of some substances may possess permanent magnet characteristics because of an imbalance between orbits and spins. These atoms act like tiny magnets, called dipoles, and are attracted by strong magnets. Substances in which this attractive effect exceeds the diamagnetism common to an atoms show the property of paramagnetism. In the atoms of ferromagnetic substances there are unpaired electrons whose spins are oriented in the same way. The common metals iron, cobalt, and nickel and the rare earth elements gadolinium and dysprosium show strong ferromagnetic properties. Some alloys of these and other elements, as well as certain metallic oxides called ferrites, also exhibit strong ferromagnetic properties. The inner quantum levels, or shells, of the atom structures of most elements contain only paired electrons. The highest quantum level, or outer shell, of each of the noble gases (except helium) consists of a stable octet of electrons made up of four electron pairs. The atoms of other elements achieve this stable configuration by forming chemical bonds. Only in certain transition elements that have Each iron atom lias four inner-shell electrons. unpaired 468 CHAPTER 19 incomplete inner shells do unpaired electrons result in ferromagnetic properties. The electron configuration of the iron atom, Figure 19-4, shows four unpaired electrons in the third principal quantum level. The similarly oriented spins of these electrons, enhanced by the influence of nearby atoms in the metallic crystal, account for iron's 26eC'ft'lnSwit\ strong ferromagnetism. . ' From the preceding discussion, it would seem that ( ectrpnswill -sJ)!n every piece of iron should behave as a magnet. However, such is not the case. Atoms are grouped in microscopic magnetic regions called domains. The atoms in each domain are magnetically polarized parallel to a crystal axis. In a polycrystalJine specimen, ordinarily these axes (and the domains) are oriented in all possible directions. The Figure 19.4. The iron atom has domains effectively cancel one another and the net magstrong ferromagnetic properties. netism is essentially zero. In Figure 19-5 the polarity of each domain in an unmagnetized material is represented by an arrow. When a ferromagnetic material is placed in an external magnetic field, two effects occur. The domains more favorably oriented in this magnetic field may increase in size at the expense of less favorably oriented adjacent domains. Other domains may rotate in order to become more favorably oriented with respect to the external field. The material becomes magnetized. If the domain boundaries remain extended to some degree even after the external magnetizing force is removed, the material is said to be "permanently" magnetized. When the direction of magnetization of a magnetic domain is rotated by an external magnetic field, it must be understood that the material of Figure 19-5. The domains of an un magnetized ferromagnetic subthe domain does not change its position in the specimen. stance are polarized along the It is only its direction of magnetization that changes. crystal axes. Dots and plus signs When the temperature of a ferromagnetic material is represent arrows going out of and raised above a certain critical value, the domain regions into the page, respectively. disappear and the material becomes paramagnetic. This temperature is known as the Curie point. It is usually lower than the melting point of the substance. The Curie points for some ferromagnetic substances are given in Table 19-1. When a single crystal of iron is sprinkled with colloidal Table 19-1 particles of iron oxide, the microscopic domains become CURIE POINTS OF FERROMAGNETIC ELEMENTS visible. Using this technique, physicists are able to photograph magnetic domains and observe the effects of exterElement nal magnetic fields on them. Typical photomicrographs of magnetic domains are shown in Figure 19-6. iron no°c cobalt A recent magnet technology that makes use of a group 1131°C nickel 358°C of ferromagnetic substances known as terrifes yields strong 16QC gadolinium hard magnets with unique properties. Ferrites are iron oxides combined with oxides of other metals such as manga- o \~ 0 1- MAGNETIC EFFECTS 469 Figure 19-6. Photomicrographs of magnetic domains. nese, cobalt, nickel, copper, or magnesium. The combined oxides are powdered, formed into the desired shape under pressure, and fired. The ferrites have very high electric resistance, a property that is extremely important in some applications of ferromagnetic materials. The originallodestone, commonly called magnetic iron oxide, is a material of this type. Chemically it is a combination of iron(II) oxide, FeO, and iron(IlI) oxide, FeZ03' Its formula is considered to be Fe(FeOzh. like poles repel 19.3 Force Between Magnet Poles The fact that iron filings cling mainly to the ends of a bar magnet indicates that the magnetic force acts on the filings primarily in these regions, or poles; it does not mean that the middle r' region of the magnet is unmagnetized. The pole that points toward the north when the magnet is free to swing about a vertical axis is commonly called the north-seeking pole, or N pole. The opposite pole, which points toward the south, is called the south-seeking pole, or 5 pole. Suppose a bar magnet is suspended as shown in Figure 19-7. When the N pole of a second magnet is brought near the N pole of the suspended magnet, the two repel each other. A similar action is observed with the two S poles. When the S pole of one magnet is placed near the N pole of the other magnet, they attract each other. Such experiments show that like poles repel and unlike poles attract. Magnets usually have two well-defined poles-one N and one S. Sometimes long bar magnets acquire more than two poles, and an iron ring may have no poles at all when magnetized. Physicists have long speculated about the existence of single-pole magnetic particles called monopoles. Known magnetic poles, however, always come in pairs called dipoles. The most elementary magnet has an S pole and an N pole. If cut in half, each half is found to be dipolar. A magnet has an S pole for every N pole. An isolated N pole of unit strength is sometimes assumed in "thought" experiments. A unit pole may bethought of as one that repels an exactly similar pole, placed one centimeter away, with a force of 10--" N. Figure 19-7. Like poles repel. Unlike poles attract. Experimental evidence of the possible existence of magnetic monopoles has been reported but not verified. Physicists believe that proof of the existence of monopoles could help verify some of the basic concepts of physics. 170 CHAPTER The quantitative expression for Coulomb's law of magnetism is M1M2 F = k . Compare this d2 equation with those in Sections 3.11 and 16.8. The first quantitative study of the force between two magnetic poles is generally credited to Coulomb. He found this magnetic force governed by the same inversesquare relationship that applies to gravitational force and electrostatic force. Coulomb's law of magnetism is; The force between two magnetic poles is directly proportional to the product of the strengths Glass S!~___Needlefloalstoright of the poles and inversely Figure 19-8. The path followed by independent N pole. IAI IBI Figure 19-9. (A) The path taken by an independent N pole in a magnetic field suggests a line of flux. (8) Magnetic flux about a bar magnet. proportional to the square of the distance between them. The force is one of repulsion or attraction, depending on whether the magnetic poles are alike or different. Fields of Force In Section 16.9 we described the electric field of force near an electrically charged object. Electric forces are not the only forces that act on charged particles. Sometimes we observe the effect of a force that is both perpendicular and proportional to the velocity of a moving charge. This force identifies a magnetic field. A dipole magnet in such a region of space experiences a torque. We speak of a magnetic field in the space around a bar magnet in the same way we speak of an electric field around a charged rod. Furthermore, we can represent a magnetic field by lines of flux, just as we represented an electric field by lines of force. The behavior of our imaginary independent N pole in a magnetic field can be approximated by using a magnetized darning needle as illustrated in Figure 19-8. The needle is supported by cork so that it floats with the N pole extended below the surface of the water. The 5 pole is far enough removed to have negligible influence on the movement of the needle. A bar magnet placed under the glass dish with its N pole near the needle causes the floating magnet to move along a path that approximates the path an isolated N pole would follow. The path of an independent N pole in a magnetic field suggests a line of flux. A line of flux is a line so drawn that a tangent to it at any point indicates the direction of the magnetic field. Flux lines are assumed to emerge from a magnet at the N pole and to enter the magnet at the S pole. Every flux line is a closed path running from S pole to N pole within the magnet. See Figure 19-9. The lines of flux perpendicular to a specified area in the magnetic field are collectively called the magnetic flux, for which the Greek letter q:, (phi) is used. The unit of magnetic flux is the weber (Wb). The magnetic flux density, B, is the number of flux lines per unit area that permeates the magnetic field. The flux density B is a vector quantity; the direction of B at any point in the magnetic field is the direction of the field at that point. 19.4 Magnetic the floating magnet in this experiment is approximately that of an 19 B~ "'fA f 471 MAGNETIC EFFECTS Flux density is expressed in webers per square meter (Wb/m2). The flux density determines the magnetizing force at any point in the magnetic field. The weber per meter- is also called the tesla (T). = 1 tesla 1 weber/meter2 The measurement of these quantities is in Section 19.9. Flux lines drawn to indicate how tiny magnets would behave when placed at various points in a magnetic field provide a means of mapping the field. A line drawn tangent to a flux line at any point indicates the direction a very small magnet would assume if placed there. An arrowhead can be added to the tangent line to indicate the direction in which the N pole of the tiny magnet would point, thus giving the direction of the magnetic field, and the B vector, at that point. Using a suitable scale of flux lines per unit area perpendicular to the field, the flux density, B, at any point can be illustrated. Selection of a number of lines to represent a unit of magnetic flux is arbitrary. Usually, one flux line per square meter represents a flux density of 1 Wb/m2. In this sense, one line of flux is a weber. The magnetic field near a single bar magnet is suggested by the pattern formed by iron filings sprinkled on a glass plate laid over the magnet. A photograph of this field pattern is shown in Figure 19-10. Using a similar technique, the magnetic fields near the unlike poles and near the like poles of two bar magnets are illustrated in Figure 19-11. Observe that the magnetic force acting on the two unlike poles is one of attraction and that acting on the two like poles is one of repulsion. Figure 19-12 similarly illustrates an end-on view of the magnetic field between the poles of a horseshoe magnet. 19.5 Magnetic Permeability In Section 19.4 we described the effect of a magnetic field of force on iron filings and on a magnetized needle as experienced through glass ,)\' '~:' Imaginary lines of magnetic flux are useful for mapping magnetic fields. Figure19-10. Iron filings near a single bar magnet. ",'", '/ " I''i'~~!?!/::"7",,:-::-=,~- ~:~ "'''" ~(\~)): J ',1'~'17: '1 I l~ ;<:'-::;:'~'>J'\\\\','I,: \\I\\ fl, , ,:{, ' ' :, ''';:,..,"___~" ::" , ":'\\'\il' , , , , ! ~.:£"c::->-' ''-''",, /.!'.:, ' j, ",, / ~ "~'\\\ "" \ Ib',//. ::--C~" ," ' . \ "' ' \ \1" I /'j.../- " :..,-.,.."""'-"'-...: "'-...:, ,,,,\, I'..>,"', :' :;,' ,(1'.":--' -"'-.-.'-"-.,:_" -'.:>"\.,...,~'" . ~ ,'.'I '/ .~, ,,', ~:---. !'\"" .,. 'C(' '~ '~' :. \~\" 1;';f/~"-;-c-2?~' ~,~ ~/ ~ ~~ " ' , . , '-' . -" ~:.::~~~~-:,¥.::- ~~ ~ ~ ,- ,,~~~*~,.,:}tMi~%\RI'I~~~~:';-;'~':"~:T ',f::.:::;..' ~~~~':S:::-c-", '[;~~--;.~: -'-' ~'~'-::-~:.' " , ...',~,,\\'iW..i :';:t'C~~~ ~~~~, ~~-:.~;~,~;;;;,1'f:i'f,.,~!i;,,:,: ~ ,~:7-~~~-:. .,,0.-00,. t.,-' ..- _~~ .~"/ -"'-'i)'. ' .,'\;\:~ \~' ''\'~..:'-., ':" ,(,;,:','; ~:; :;;@.~i: ~:; :,:, !.:~',~(\{;~~.~~2\~'~l ~~?:~-~ ...," /,//'/-' ,/; I"'\ . ,.;., , ,.'"...... rif '_" ; "j ',..,' :/. - , '." , , r \\ II. "'/'- /: ,,",/./' "('"/~." ,t,..;,V. r ',I '.'i '.. '~('0~~--?!';:'~': ~ ~" "\\. 1 'I' 1' .' ',' .\' ;"/;, ;..-,I;/),! ::-\,;<~,\"i..'\:>' L,-::riI(.':-/-; . :::"':"'.,I','u, '.~1, .,,,,.,.,,, \, :'>:..",-",_~,~ .>_',./ .',_ "''__ 1,! i, '..'."'" ,'.-'(.:.., --':' -. ,., ' ' ,.," , ...l\ j""." ,: ',,' ,, """\," "',.\,.".": '\\;'\.,_. ,'C,~",' I. ~.: "" ;:~':-""" c>_.-, ,'.CO',.,. ~'.~..\ "_-"'...~_ _ ",...",'iZ"':'-c,'~_-y_:~. ''j''<,',.. '-'I" ":,~__ CHAPTER 19 472 Figure 19-11. Iron filings are shown near unlike poles of two bar magnets in (A) and near their like poles in (B). 16) IAI IA) Figure 19-12. (A) Iron filings near the poles of a horseshoe magnet, end view. (B) An idealized drawing of (A) showing lines of flux. In a practical sense, all materials except those that are ferromagnetic can be considered magnetically inert. In a magnetic fie/d, they behave just like air. 16) and water. Nonmagnetic materials in general are transpar- ent to magnetic flux; that is, their effect on the lines of flux is not appreciably different than that of air. Theproperty of a material by which it changes the flux density in a magnetic field from the value in air is calledits permeability, f.L. Permeability is a ratio of flux densities and is without dimension. The permeability of empty space is taken as unity and that of air as very nearly the same. The permeabilities of diamagnetic substances are slightly less than unity; permeabilities of paramagnetic substances are slightly greater than unity. Permeabilities of ferromagnetic materials are many times that of air. If a sheet of iron covers a magnet, there is little magnetic field above the sheet. The flux enters the iron and follows a path within the iron itself. Similarly, an iron ring placed between the poles of a magnet provides a better path than air for the magnetic flux. This effect is illustrated in Figure 19-13. The flux density in iron is greater than it is in air; therefore, iron is said to have a high permeability. The permeabilities of other ferromagnetic substances are also very high. MAGNETIC EFFECTS 473 Magnetic lines~ c ; c f , ,, Suppose a bar of soft iron lies in a magnetic field, as in Figure 19-14. Because of the high permeability of the iron, the field is distorted and the magnetic flux passes through the iron in preference to the air. Under these circumstances the soft iron bar becomes a magnet with end A as the 5 pole and end B as the N pole. Such a bar is said to be magnetized by induction. Magnetism produced in a ferromagnetic substanceby the influellceof a magneticfield is called induced magnetism. A Figure 19-13. At left. magnetic flux crosses the air gap between the poles of a magnet. At right, magnetic flux follows the soft iron ring, which is more permeable than air. , ~ If the magnetic field is removed by withdrawing the two bar magnets, most of the induced magnetism will be lost. Magnets produced by induction are known as temporary magnets. A piece of hardened steel is not so strongly magnetized by induction but retains a greater residual magnetism when removed from the induction field. There is no significant difference in the process if the iron bar in Figure 19-14 is brought into contact with one of the magnet poles. The magnetization process is somewhat more efficient due to the reduction of the air gap. See Figure 19-15. 19.6 Terrestrial Magnetism Suppose the earth contained a great bar magnet. See Figure 19-16. It would produce a magnetic field similar to its actual field. Over most of the earth's populated surface the north-seeking pole of a compass points northward. Although it is the south pole of our fictitious magnet that attracts the N pole of the compass, the pole region is conventionally called the north magnetic pole because it is located in the northern hemisphere. Similarly, the pole region in the southern hemisphere is called the south magnetic pole. The earth's magnetic axis does not coincide with its polar (geographic) axis, but is inclined to the polar axis at a small angle. The north magnetic pole, at latitude 73°N and longitude 100oW, is about 2000 km (1200 miles) south Figure 19-14. An iron bar magnetized by induction. , Figure 19-15. The nail becomes magnet by induction. Are the tacks also magnets? a 474 CHAPTER Magnetic field____ 19 Electric current Figure 19-16. The magnetic field of the earth may be produced by electric currents within its fluid core. The field is oriented as though the earth contained a large magnet passing through its center, with the magnetic axis slightly inclined with respect to the axis of the earth. of the north geographic pole. The south magnetic pole is located in Antarctica near the Ross Sea. Thus from most locations on the earth, the N pole of the compass needle does not point to the true geographic north. At any surface location the angle between magnetic north and the true north is called the declination, or variation. In the region of Los Angeles the compass variation is about 15°E. That is to say a compass needle points about 15° to the east of true north. In the region of Boston the variation is about 15°W. Cincinnati, Ohio, is located very near the line of zero declination. Here the compass needle points to the true north and the variation is 0°. A compass needle mounted on a horizontal axis and provided with a means of measuring the angle the needle makes with the horizontal plane is called a dipping needle. At certain places on the earth's surface, about midway between the magnetic poles, the angle of dip is zero and the needle is horizontal. A line drawn through a succession of such points identifies the magnetic equator. The angle of dip is 90° at the magnetic pole. The dip, or deviation between the equilibrium position of a dipping needle and the horizontal, is known as the magnetic inclination. In 1600 the English physicist William Gilbert (1540?1603) published his scientific treatise De magnete, which deals with the magnetism of the earth. This is one of the earliest publications on the experimental treatment of a scientific topic. Gilbert inferred that the earth behaved as a large magnet because the interior consisted of permanently magnetic material. Today scientists believe the core of the earth is too hot to be a permanent magnet and is fluid rather than solid. , " MAGNETIC 475 EFFECTS The German physicist Karl Friedrich Gauss (1777-1855) showed that the magnetic field of the earth must originate inside the earth. In 1939 the American theoretical physicist Walter M. Elsasser suggested that the earth's magnetic field results from electric currents generated by the flovv of matter in the earth's fluid core. See Figure 19-16. Today physicists believe that the magnetic field is due primarily to electric currents within the earth, but they have not yet established the origin of these currents. c c f f Electric current loops inside the enrth are responsiblefor its magnetic field. f 19.7 The Magnetosphere Because space vehicles now travel to the outer limits of the earth's atmosphere and beyond, there is a growing interest in a region of the outer atmosphere known as the magnetosphere. Located beyond 200 km, the magnetosphere is the region in which the motion of charged particles is governed primarily by the magnetic field of the earth. At lower altitudes, where the density of the atmosphere is much greater, the motion of charged particles is controlled largely by collisions. The magnetosphere on the side facing the sun extends beyond the earth's surface approximately 57000 km, or about 10 earth radii. On the side away from the sun, the magnetosphere probably extends outward for hundreds of earth radii. See Figure 19-17. The elongated shape results from the influence of the onrushing solar wjnd, or solar plasma. The solar wind, consisting mainly of protons and electrons emitted by the sun, compresses the magnetosphere on the side nearest the sun. In 1958 regions of intense radiation were discovered within the magnetosphere by a team of physicists headed f r I I I , Figure 19-17. The magnetosphere of the earth. The overall radiation regions are shown in color. The inner and outer Van Allen belts of intense radiation are the dark regions ranging outward to approximately 4 earth radii. f , r I Solar I I wind ~~J\cE'''h "- I VanAllen radiation bells ~ ~ r-. " " 10 5 0 5 0 15 " " Earth 30 30 40 radii CHAPTER 19 476 Auroral displays over the polar regions are related to fhe escape of energeticparticles from fhe radiation belts. QUESTIONS: by Dr. J. A. Van Allen (b. 1914). These regions, now known as the Van Allen radiation belts, contain energetic protons and electrons trapped by the earth's magnetic field. Those trapped in the inner belts probably originate in the earth's atmosphere; those trapped in the outer belts probably have their origin in the sun. When these intense radiation belts were first discovered, scientists were concerned about the serious threat they appeared to present to space travel. Today, astronauts journeying into outer space are able to pass quickly through these regions with adequate protection from the Van Allen radiation. GROUP A 1. (a) What are natural magnets called? (b) Is this term appropriate? Explain. 2. Describe the two electron motions that affect an object's magnetic properties. 3. What is a magnetic domain? 4. Why are iron atoms so strongly affected by magnetic fields? 5. When a magnetized steel needle is heated strongly in a bunsen burner flame, it becomes demagnetized. Explain why. 6. What indicates that a piece of iron is magnetic-its attraction to or repul. sian from another piece of iron? 7. Describe the magnetosphere. 8. (a) What is the minimum number of poles for a magnet? (b) Can a magnet have three poles? Explain. 9. (a) When you break a magnet in half, how many poles does each piece have? (b) How small would the pieces have to be for this not to be true? 10. What is the difference between the angles of declination and inclination? GROUP B 11. VVhat is the difference behveen a paramagnetic and a ferromagnetic material? 12. What do we mean when we say a piece of paper is magnetically transparent? 13. Why does a very strong magnet attract both poles of a weak magnet? 14. (a) How does solar wind affect the shape of the earth's magnetic field? (b) Name two other effects of charged atmospheric particles on the earth's magnetic field. 15. A strong magnet in a junkyard can lift a car; what does this tell you about the relative strength of the magnetic and gravitational forces on the car? 16. What happens on a subatomic level when a magnet attracts a steel needle? 17. If a small magnet is repeatedly dropped, it becomes demagnetized. Explain what is happening subatomically. IS. Compare and contrast the effects of electrostatic and magnetic forces. 19. Sir William Gilbert believed the earth contained an iron core that was a huge permanent magnet. Give some evidence to refute this theory. 20. What happens when you pass a magnet across a computer floppy disk? ELECTROMAGNETISM 19.8 The Link Between an Electric Current and Magnetism It can be easily demonstrated that electrostatic charges and stationary magnets have no effect on one an- c , f' , f r f f " MAGNETIC EFFECTS 477 other. However, in 1820 Hans Christian Oersted (er-stet) (1777-1851), a Danish physicist and professor of physics at the University of Copenhagen, observed that a small compass needle is deflected when brought near a conductor carrying an electric current. This was the first evidence of a long-suspected link between electricity and magnetism. Oersted discovered that forces exist behveen a magnet and electric charges in monon. His famous experiment is so significant that a brief description of it is in order. A dry cell, compass, switch, and conducting wire are arranged as shown in Figure 19-19(A). With the switch open, a straight section of the conductor is supported above the compass in the vertical plane of the compass needle. In Figure 19-19(B) the dry-cell connection is such that the electron flow will be from north to south. When the switch is closed, the N pole of the compass is deflected toward the west. When the drv-cell connections are reversed so electron flO\\' is from south to north, the N pole of the compass is deflected to the east, as in Figure 1919(C). It is evident that a magnetic field exists in the rcgimz near the conductor when the circuit is closed. Furthermore, the direction of the field is dependent 011the direction of the current Figure 19-18. Hans Christian Oersted studied medicine before becoming professor of physics at the University of Copenhagen in 1806. Several years before he performed his famous experiment. he predicted that a link between electricity and magnetism would be found. ill the conductor. Figure 19-19. The Oersted experiment as viewed from above. In ,-r- I /11\ " r: ~-1;: Sw ,I -.-J (AJ ,-,--- ,BJ each j diagram is located the compass needle below the conductor. ,-I Sw ~ (OJ If the experiment is repeated with the conductor placed below the compass needle, the compass deflection is opposite to that in the first experiment. This suggests, but does not prove, that the magnetic field encircles the conductor. 19.9 Magnetic after Oersted's Field and a Charge in Motion discovery, the French physicist Shortly Ampere determined the shape of the magnetic field about a conductor carrying a current. He had discovered that forces exist between two parallel conductors in an electric circuit. If the two currents are in the same direction, the force is one of attraction; the force is one of repulsion if the currents are in opposite directions. See Figure 19-21. In a quantitative sense, two long, straight, parallel conductors of length I separated by a distance d and carrying Figure 19-20. Andre Ampere, the French physicist for whom the unit of electric current is named, did fundamental work in electromagnetism. CHAPTER 19 478 currents hand 12will each experience a force F of magnitude 2k 11112 F~ d The constant k is exactly 10-7 N/A2. If I} and 12 are expressed in amperes and land d in meters, the force F is given in newtons. (~,)x(m'~'A)=N "\ ,- ,-I' I ,- 1 j . '11 F 11 Figure 19-21. l' 1 \ ,-, \ F $. $. Forces between parallel currents (A) in the same direction and (8) in opposite di- ,A, rections. ,s, Because these attractive and repulsive forces between current-carrying conductors are directly proportional to the currents in the conductors, they provide a precise method of defining the unit of current, the ampere. In this sense, the ampere may be defined as the current in each of two long parallel conductors spaced one meter apart that causes a magnetic force of 2 x 10-7 newton per meter length of conductor. Following this scheme, charge (an ampere-second) of electric the coulomb as a quantity of may be defined as the quantity chargethat passesa given point on a cOtlductor in one second when the conductor carries a constant current of one ampere. Ampere investigated the magnetic fields about conductors to find an explanation of the magnetic forces. Suppose a heavy copper wire passes vertically through the center of a horizontal sheet of stiff cardboard. When the ends of the vertical conductor are connected to a dry cell, iron filings sprinkled over the surface of the cardboard form a pattern of concentric circles around the conductor. See Figure 1922. If a small compass is placed at successive points around a circle of filings, the needle always comes to rest MAGNETIC 479 EFFECTS , , ,-I I) j I f f I f l Figure 19-22. The magnetic field encircling a current in a straight conductor. Sw tangent to the circle and with the same tangential orientation of its N pole. H the direction of current in the vertical conductor. is reversed, the compass needle again becomes aligned tangent to the circle of filings, but with its N-pole orientation reversed. From these observations we conclude that a magnetic j1:eldencircles an electric charge in 1110tion.The lines of flux are closed concentric circles in a plane perpendicular to the conductor with the axis of the conductor as their center. The direction of the magnetic field is everywhere tangent to the flux and is dependent on the direction of the current. Ampere devised a rule, known today as Ampere's rule, for determining the direction of the magnetic field around a current in a straight conductor when the direction of the electron flow is known. Ampere's rule for a straight conductor: Grasp the conductor in the left hand with the thumb extended in the direction of the electron flow. The fingers then will circle the conductor in the direction of the magnetic flux:. See Figure 19-23. The flux density, B, also called the magnetic inductiOll, at any point in the magnetic field of a long straight conductor carrying a current, l, is directly proportional to the current in the coltductor and inversely proportional to the radial distance, r, of the point from the conductor. B ~ 2k- MagI/die phenomena are interpreted ill tenns of the forces associated with electric charges in motia/I. The left-hand rule for a straight cUllductor illdicates the direction of the magnetic flux surrounding the conductor. I [ r The constant k again is 10-7 N/A2. When I is given in amperes and r is in meters, B is expressed in newtons per ampere meter, which is equivalent to webers per square meter. In Section 19.4 flux density is defined in terms of the lines of flux per unit area that permeate the magnetic field. Electron (e-j flow Magnetic field Figure 19-23. Ampere's rule for a straight conductor. CHAPTER 19 480 In this sense the expression Thus '" for flux density is B = 1>/A. ~ BA When B is expressed in newtons per ampere meter, the unit for 1>, the weber, can be shown to be 1 newton-meter per ampere: N Wb= ( A'm ) x(m2)=- N'm A Whether 1> is expressed in webers or newton meters per ampere and B is expressed in webers per square meter or newtons per ampere meter is a matter of convenience in each situation. Observe that the definition of B given in Section 19.4 is based "On the force exerted on an isolated unit pole. An isolated pole exists only in the fiction of a thought experiment; consequently, measurements based on this definition lack precision. The more practical definition given above involves quantities that can be measured precisely and is therefore generally preferred. Figure 19-24. The magnetic field through a current loop. 19.10 Magnetic Field and a Current Loop Keeping Ampere's rule in mind, let us consider a loop in a conductor carrying a current. The magnetic flux from all segments of the loop must pass through the inside of the loop in the same direction; that is, the face of the loop must show polarity. See Figure 19-24. ,-I j N ,-I j (A) A magnetic lube is an imaginary tube bounded by magnetic lines. It a/waifs links the current that prodl/ces the field. (B) This loop magnet can be made stronger if the flux density can be increased. Because the magnetic field around a conductor varies with the current, the flux density can be increased by increasing the magnitude of the current in I [ c r f t I I r MAGNETIC 481 EFFECTS the conducting loop, by forming addihonalloops in the conductor, or by both. A linear coil of such conducting loops takes the form of a helix and is called a sole/wid. The cylindrical column of air inside the loops, extending the length of the coil, is called the core. When a current is in a solenoid, the core of each turn (loop) becomes a magnet; the core of the solenoid is a magnetic tube through which practically all the magnetic flux passes. See Figure 19-25. Because a solenoid conducting an electric current has the magnetic properties of a bar magnet, its polarity can be determined by means of a compass. However, the magnetic flux in the core of the solenoid is derived from the magnetic field of each turn of the conductor. Thus Ampere's rule is modified to adapt it to this special case of the solenoid. Ampere's rule for a solenoid: Grasp the coil in the left hand with the fingers circling the coil in the direction of the electron flow. The extended thumb will point in the direction of the N pole of the core. See Figure 19-26. 19.11 The Electromagnet A solenoid with a core of air, wood, or some other nonmagnetic material does not produce a very strong electromagnet because the permeability of all nonmagnetic substances is essentially equal to that of air-unity. Substitution of such materials for air does not appreciably change the flux density. Soft iron, on the other hand, has a high permeability. If an iron rod is substituted for air as the core material, the flux density is greatly increased. Strong electromagnets therefore have ferromagnetic cores with high permeability. For a given core material, the strength of the electromagnet depends on the magnitude of the current and the number of turns. In other words, its strength is determined by the number of ampere-turns. 19.12 The Galvanometer Suppose we form a wire loop in a vertical plane, place a compass needle (free to rotate in a horizontal plane) in the center of it, and then introduce a current into the loop. The needle will be deflected. If we increase the number of turns sufficiently, even a feeble current will produce a deflection of the needle. Such a device, called a galvanoscope, may be used to detect the presence of an electric current or to determine its direction. A simple galvanoscope is shown in Figure 19-28. A more versatile instrument for detecting feeble currents is the galvanometer, the essential parts of which are shown in Figure 19-29. A coil of wire wound on a soft iron core is pivoted on jeweled bearings between the poles of a I .~ I I .~ I s Figure 19-25. Magnetic field about a solenoid. s N .1 Figure 19-26. Ampere's rule for a solenoid. Figure 19-27. A superconducting electromagnet. In operation, the eight-foot cylinder is immersed in liquid helium (-232°C). At this temperature the niobium-titanium strips imbedded in the copper coils lose all electric resistance and the magnet produces a force field up to 5000 times greater than that of the earth. j.~ ..~ CHAPTER 19 482 Figure 19-28. scope. Because a magnetic field exerts forces on moving charges, it exerts torques on current-carrying coils. Scale Permanent magnet permanent horseshoe magnet. The coil becomes a magnet when current is in it. The instrument then has two magnets: a permanent horseshoe magnet in a fixed position and an electromagnet free to turn on its axis. Electric connections to the coil are made through two control springs (not shown), one above and one below the coil. These coiled springs also restrain the rotational motion of the coil so that the attached pointer returns to the zero scale position when no current is present in the coil. This zero position is often located at the midpoint of the scale, as in Figure 19-29. When there is a current in the movable coil, its core is magnetized. The poles of the core are then attracted and repelled by the poles of the pennanent magnet. A torque acts upon the coil and the coil rotates in an attempt to align its plane perpendicular to the line joining the poles of the permanent magnet. As the coil rotates, however, it does work against the two control springs. Its final position is reached when the torque acting on it is just neutralized by the reaction of the springs. Since the permanent field flux is constant, the torque on the coil is proportional to the current in it. We may assume, for small movements of the coil, that the reaction of the springs is proportional to the deflection angle. When the coil reaches its equilibrium position, these two opposing torques are equal, and the deflection angle of the coil is therefore proportional to the current in it. The scale of the galvanometer is marked at intervals on either side of the zero center. Readings are made on this scale by means of a small, lightweight pointer attached to the coil. For a coil current in one direction, the needle deflection is to the left. If the current direction is reversed, the needle is deflected to the right. The galvanometer is a sensitive instrument for detecting feeble currents of the order of microamperes. For transla~ tion of a reading into absolute current values, the current sensitivity of the specific instrument must be known. Current sensitivity is usually expressed in microamperes per scale division. The pointer deflection, d, of a galvanometer is proportional to the current, 1M, in the coil 1M 0:: d kd [M or ~ Coil and 19-29. The basic components of a moving-coil galva- Figure nometer. where k is the current scale division. k = 1M d sensitivity in microamperes per '- , f r r r I MAGNETIC EFFECTS 483 The moving coil of the galvanometer has resistance. By Ohm's law, a potential difference appears across the resistance of the meter when a current is in the coil. We can express the voltaxe sensitivity of the instrument since it must be equal to the product of the meter resistance and the current per scale division. Voltage sensitivity = where RM is the resistance of the meter movement. Volt. age sensitivity is given in microvolts per scale division. If provision is made to prevent excessive currents from entering the coil, the galvanometer can be adapted for service as either a d-c ammeter or d-c voltmeter. The following examples illustrate calculations involving the galvanometer. Figure19-30. Sensitive galvanometers use a mirror to indicate the position of a suspended coil by producing an image of a scale viewed through a telescope or by reflecting a beam of light onto a scale EXAJIPLE A galvanometer has a current sensitivity of 2.50' x 10'~jJ..A, and the scale goes from - 50' to 0 to 50, with 0' at the very center. Calculate the current in amperes that is passing through the coil of the instrument when the reading is 18.5 on either side of zero. .r 2500 I'-A 50'.0'divisions k= d = 18.5 "'!I" Bnsic equation Unknown Cin'r~ - . i 1M = I" kd divisions Solution I .. Working- equatIOn: ( [M = kd = (2500 I'-A)(lO-O AII'-A)(18.5 ~.Odiv EXAMPI.F If the meter resistance in the previous what is the voltage across the fully deflected meter? div) = 9.25 X 10-4 A example is ~~ I Ir'!!!!. JI""'."__ ( .Ivcn "~' r k = 50'.0' ,uA/div d = 50.0' div RM 10,0 !l ~ ='-=''''--"JI Unknown V" Basi(~ e(IlJation~ VM=lMRM 1M=kd !"!'!I iI oJ; CHAPTER 19 484 Solution Working equation: ~ ~ (50.0I'Aldiv)(IO-' AII'A)(50.0 div)(lO.O fJ) 2.50 x 10-' V PIL\(:TI(]~ IJIl()BL~MS 1. What magnitude of current will produce a full-scale deflection of a galvanometer with exactly 40 scale divisions and a sensitivity of 30.0 fLA per scale division? Ans. 1.20 x 10-3 A 2. What is the voltage across the fully deflected galvanometer in Problem 17 (The meter resistance is 8.50 n.) Ans. 1.02 x 10-2 V 19.13 The d-c Voltmeter The potential difference across a galvanometer is quite small even when the needle is fully deflected. If a galvanometer is to be used to measure voltages of ordinary magnitudes, we must convert it to a high-resistance instrument. The essential parts of a d-c voltmeter are shown in Figure 19-31. d-cvoltmeter 1.5 ,.0 2.0 0' Electrons which flow through the voltmeter pass through the rear coiled control spring and into the windingsonthemovabJecoil Coils of high resistance wire -,"-"il c'ilc__ E " [7., ' iL'3J.N :"1 ,'''iI~: Electrons from the movable coil windings pass through the front control spring, and through highresistancecoilstothe positive terminal the The high resistance coils permit only a few electrons to flow through the movable coil of a voltmeter Figure 19-31. The construction of a d-c voltmeter showing the high resistance in series with the windings of the movable coil. If a high resistance is added in series with the moving coil, most of the potential drop appears across this series resistor, or multiplier. Since a voltmeter is connected in parallel with the part of a circuit across which the potential differ- , I MAGNETIC EFFECTS 485 ence is to be measured, a high resistance prevents an appreciable loading effect. By the proper choice of resistance, the meter can be calibrated to read any desired voltage. Suppose we convert the galvanometer used in the examples in Section 19.12 to a voltmeter reading 15.0 volts on full-scale deflection. The current required for full deflection has been found to be 2.50 x 10-3 ampere, and the resistance of the meter coil is 10.0 ohms. We must determine the value of the resistor Rs to be placed in series with the moving coil. Figure 19-32 illustrates this problem. Since RM and Rs (of Figure 19-32) are in series, Then V = IMRM + IMRs V Rs = RM 1M Rs 15.0 V ~ 2.50 x 10-3 A - 10.0 n Rs = 5990 fi, value of the series resistor Observe that the total resistance between the terminals of the meter is 60'00 ohms. The voltmeter sensitivity is frequently expressed in terms of ohms per volt. When the ohms-per-volt sensitivity of a voltmeter is known, we can quickly estimate the loading effect it will have when placed across a known resistance component of a circuit. For example, at 400 ohms per volt, our meter, which reads from 0 to 15 volts, has 6000 ohms between the terminals. If it were placed across resistances greater than about 600 ohms, the loading effect would result in serious meter errors. 19.14 The d-c Ammeter We could use the basic galvanometer in Section 19.12 as a microammeter by calibrating the graduated scale to read directly in microamperes. However, the meter would not be useful in circuits in which the current exceeded 2500 microamperes. Current in the resistance of a galvanometer coil produces ]2R heating, and an excessive current would burn out the meter. To convert the galvanometer to read larger currents, an alternate (parallel) low-resistance path for current, called a sllunt, must be provided across the terminals. By the proper choice of shunt resistance, we can calibrate the meter to read over the required range of current magnitudes. See Figure 19-33. Suppose we wish to convert the same galvanometer to an ammeter reading 10.0 amperes full scale. As before, the current required for the full deflection of the moving coil is 2.50 x 10-3 ampere and the resistance is 10.0 n. We Galvanometer mav.bl.coil Seri.'r...i'tar . RM =10.051 1M =0.002 50A Figure 19-32. Converting a galvanometer to a voltmeter. 486 CHAPTER 19 , 4 . Electrons from the movable coilwindingspasslhrough the front control spring and The few electrons which flow through the coil of the ammeter pass througl1 the rear CDiled conlrol spring and into the windings on ttle movable coil theconn~tingwiret()the positiveterminaJ Mostoftheelectronsentering the ins!rument Ilow through Ihe low resislance shunt Figure 19-33. The construction of a d-c ammeter showing the low resistance in parallel with the windings of the movable coil. must determine the resistance of the shunt across the coil. Figure 19-34 applies. Since RM and Rs are in parallel, IMRM But Galvanometer moving coil Then R s -- Rs " '" Shunt,e<istQr Figure 19.34. Converting a galvanometer to an ammeter. = Is = Rs = = IsRs IT - 1M IMRM IT 2.50 X 10-3 A x 10.0 - to be used - 1M n 10.0 A 0.002 50 A 0.002 50 H, the value for the shunt resistor The total resistance of the ammeter is the equivalent value for 10.0 ohms and 0.002 50 ohm in parallel; it will be less than 0.002 50 ohm. This exercise demonstrates clearly why an ammeter must be connected in seriesin a circuit, and why it does not materially alter the magnitude of current in the circuit. 19.15 The Ohmmeter An ohmmeter provides a convenient means of measuring the resistance of a circuit component. A basic ohmmeter circuit is shown in Figure 19-35. Its accuracy limitation is approximately the same as r f f I- 487 MAGNETIC EFFECTS that of the voltmeter-ammeter method of measuring resistance; actually, it is a modified version of this method. The ohmmeter must be used only on a completely deenergized circuit. The ohmmeter circuit of Figure 19-35 shows a milliammeter requiring 1 mA for full-scale deflection. With an emf of 4.5 volts, by Ohm's law, 4500 ohms of resistance will provide 1 mA of current when terminals A-B are shortcircuited. A fixed resistor, R2, of 4000 ohms and a rheostat Rl1 of 0-1000 ohms are provided. To use this ohmmeter, A and B are short-circuited and RI is adjusted to give full deflection. If the emf is 4.5 V, RI will be set at 500 ohms. The pointer position at full-scale deflection is now marked as zero ohm (0 H). The rest position of the pointer is the open-circuit position with infinite p: ~A 400012 R, ~_0-1000'1 4.5V-=- 'mA (full ~cale) ~ A Figure 19.35. A basic ohmmeter circuit. resistance between A and B. This position is marked as cc u. Other resistance calibrations may be made from Ohm's law applications. For example, 4500 ohms between A and B will mean a total of 9000 ohms in the circuit and 0.5 mA of current. This mid-scale position of the pointer can be marked 4500 n. The meter, when recalibrated, will read the resistance between terminals A-B. Each time the ohmmeter is used, it is first shorted across A-B and R1 is adjusted to "zero" the meter. This operation calibrates the meter and accommodates any decrease in the terminal voltage of the battery with age. The resistance RI allows the ohmmeter to be used until jg drops below 4.0 volts. QUESTIONS: GROUP A 5. Upon what factors does the strength 1. What did Oersted discover? 2. A conductor carrying a current is arranged so that electrons flow in one segment from north to south. If a compass is held over this segment of the wire, in what direction is the needle deflected? 3. Describe a simple experiment to show the nature of the magnetic field about a straight conductor carrying a current. 4. Suppose an cIectron flow in a con- ductor passing perpendicularly through this page is represented by a dot inside a small circle when the direction of flow is up out of the page. What is the direction of the magnetic flux about this current? of an electromagnet depend? prevents the movable coil of a galvanometer from aligning its magnetic field parallel to that of the permanent magnet each time a current is in the coil? 7. (a) Why is it necessary that an amme~ ter be a low-resistance instrument? (b) Why must a voltmeter be a high~ resistance instrument? 6. What GROUP B 8. A solenoid with ends marked A and B is suspended by a thread so that the core can rotate in the horizontal plane. A current is maintained in the coil such that the electron flow is clockwise when viewed from end A B 488 9. 10. 11. 12. 13. CHAPTER toward end B. How will the coil align itself in the earth's magnetic field? A stream of electrons is projected horizontally to the right. A straight conductor carrying a current is supported paralJel to the electron stream and above it. (a) What is the effect on the electron stream if the direction of the current in the conductor is from left to right, (b) if the current is reversed? If the conductor in Question 9 is replaced by a magnet with a downward magnetic field, what is the effect on the electron stream? Why might the potential difference indicated by a voltmeter placed across a circuit load be different from the potential difference with the meter removed? Suppose the resistance of a highresistance load is to be determined using the voltmeter-ammeter method. Considering the design characteristics of ammeters and voltmeters, how would you arrange the meters in the circuit to reduce the error to a minimum? Draw your circuit diagram and justify your arrangement. Assume that the resistance of a lowresistance load is to be determined using the voltmeter-ammeter method. How would you arrange the meters in this circuit to reduce the error to a minimum? Draw your circuit diagram and justify your arrangement. PROBLEMS: GROUP A 1. Two parallel conductors 2.0 m long and 1.a m apart and carrying equal currents experience a total force of 1.6 x 10-6 N. What magnitude of current is in each conductor? 2. An ammeter that has a resistance of 0.01 ohm is connected in a circuit and indicates a current of 10 amperes. A shunt having a resistance of 0.001 ohm 19 is then connected across the meter terminals. What is the new reading on the meter? Assume the introduction of the shunt does not affect the total circuit current. 3. A galvanometer has a zero-center scale with 20.0 divisions on each side of zero. The pointer deflects 15.0 scale divisions when a current of 375 J1.A is in the movable coil. (a) What is the current sensitivity of the meter? (b) What current will produce a fullscale deflection? GROUP R 4. A galvanometer has a resistance of 50.0 n and requires 75.0 mA to produce a full-scale deflection. What resistance must be connected in series with the galvanometer in order to use it as a voltmeter for measuring a maximum of 300.0 V? 5. A galvanometer movement has a resistance of 2.5 ohms and when fully dgflected has a potential difference of 50 millivolts across it. What shunting resistance is required to enable the instrument to be used as an ammeter reading 7.5 amperes full scale? 6. A repulsive force of 9.6 x 10-4 N is experienced by each of two parallel conductors 5.0 m long when a current of 3.2 A is in each conductor. By what distance are they separated? PHYSICS ACTIVITY Try to measure the magnetic declination (if any) where you live. On a clear night, go outside with a compass and compare the direction of the compass needle with the direction of the North Star. If possible, conduct the experiment in an open space to avoid interference from local magnetic fields. I MAGNETIC EFFECTS Magnetite, a magnetic iron ore, is a natural magnet. Metals of the Iron Family and special metallic alloys and oxides are strongly attracted by magnets; they have ferromagnetic properties. Very strong magnets are made from ferromagnetic substances. Materials that are not ferromagnetic are commonly said to be nonmagnetic. Ferromagnetic materials have high permeabilities. Nonmagnetic materials in general are transparent to magnetic flux. These materials may be very feebly diamagnetic or paramagnetic. Magnetism is explained by the domain theory. Coulomb's law for magnetism is a quantitative expression for the force acting between two magnetic poles. A magnetic field, and its influence on a fictitious N pole, shows similarities to an electric field and its influence on a positive test charge. 1- 1- I VOCABUURY ammeter Ampere's rule Coulomb's law of magnetism Curie point declination diamagnetism dipping needle .. ..... SUMMARY 489 ... A charge in motion is surrounded by a magnetic field. The core of a coil carrying an electric current becomes a magnet. Strong electromagnets are produced by winding a conducting coil around a ferromagnetic core. The strength of an electromagnet depends on the number of turns of coil and the magnitude of the current in the coil. The galvanometer is the basic meter for d-c measurements. The galvanometer can be calibrated as a voltmeter by placing a high resistance in series with the galvanometer coil. It can be calibrated as an ammeter by placing a very low resistance shunt across the galvanometer coil. An ohmmeter requires a source of emf, an adjustable resistance, and a sensitive ammeter. It is essentially a voltmeterammeter method of measuring the resistance of a circuit component. .- I.U. domain electron pair ferromagnetism flux density galvanometer induced magnetism line of flux magnetic induction magnetosphere ohmmeter paramagnetism permeability solar wind solenoid voltmeter