8
CHAPTER
Magnetism
A MAGNETIC FIELD ARISES WHEN ELECTRIC CHARGE CARRIERS MOVE. CONVERSELY, WHEN AN ELECTRIcal conductor moves in a magnetic field, current flows in that conductor.
Geomagnetism
The earth has a core consisting largely of iron, heated to the extent that some of it liquefies. As the earth rotates on its axis, the iron in the core flows in convection patterns, generating the geomagnetic field that surrounds our planet and extends thousands of kilometers into space.
Earth’s Magnetic Poles and Axis
The geomagnetic field has poles, just as an old-fashioned bar magnet does. On the earth’s surface, these poles exist in the arctic and antarctic regions, but they are displaced considerably from the geographic poles (the points where the earth’s axis intersects the surface). The geomagnetic lines of flux converge or diverge at the geomagnetic poles. The geomagnetic axis that connects the geomagnetic poles tilts somewhat with respect to the geographic axis on which the earth rotates.
Charged subatomic particles from the sun, constantly streaming outward through the solar system, distort the geomagnetic field. This so-called solar wind “blows” the geomagnetic field out of symmetry. On the side of the earth facing the sun, the lines of flux compress. On the side of the earth opposite the sun, the lines of flux dilate. Similar effects occur in other planets, notably Jupiter, that have magnetic fields. As the earth rotates, the geomagnetic field “dances” into space in the direction facing away from the sun.
The Magnetic Compass
Thousands of years ago, observant people noticed the presence of the geomagnetic field, even though they didn’t know exactly what caused it. Certain rocks, called lodestones, when hung by strings, always orient themselves in a generally north-south direction. Long ago, seafarers and explorers correctly attributed this effect to the presence of a “force” in the air. The reasons for this phenomenon remained unknown for centuries, but adventurers put it to good use. Even today, a magnetic compass makes a valuable navigation aid. It can work when more sophisticated navigational devices, such as a Global Positioning System (GPS), fails.
The geomagnetic field interacts with the magnetic field around a compass needle, which comprises a small bar magnet. This interaction produces force on the compass needle, causing it to align itself parallel to the geomagnetic lines of flux in the vicinity. The force operates not only in a horizontal plane (parallel to the earth’s surface), but also vertically in most locations. The vertical force component vanishes at the geomagnetic equator, a line running around the globe equidistant from both geomagnetic poles, so the force there is perfectly horizontal. But as the geomagnetic latitude increases, either towards the north or the south geomagnetic pole, the magnetic force pulls up and down on the compass needle more and more. We call the extent of the vertical force component at any particular place the geomagnetic inclination. Have you noticed this when using a magnetic compass? One end of the needle dips a little toward the compass face, while the other end tilts upward toward the glass.
Because the earth’s geomagnetic axis and geographic axis don’t coincide, the needle of a magnetic compass usually points somewhat to the east or west of true geographic north. The extent of the discrepancy depends on our surface location. We call the angular difference between geomagnetic north (north according to a compass) and geographic north (or true north) the geomagnetic declination.
Magnetic Force
As children, most of us discovered that magnets “stick” to some metals. Iron, nickel, a few other elements, and alloys or solid mixtures containing any of them constitute ferromagnetic materials. Magnets exert force on these metals. Magnets do not generally exert force on other metals unless those metals carry electric currents. Electrically insulating substances never “attract magnets” under normal conditions.
Cause and Strength
When we bring a permanent magnet near a sample of ferromagnetic material, the atoms in the material line up to a certain extent, temporarily magnetizing the sample. This atomic alignment produces a magnetic force between the atoms of the sample and the atoms in the magnet. Every single atom acts as a tiny magnet; when they act in concert with one another, the whole sample behaves as a magnet. Permanent magnets always attract samples of ferromagnetic material.
If we place two permanent magnets near each other, we observe a stronger magnetic force than we do when we bring either magnet near a sample of ferromagnetic material. The mutual force between two rod-shaped or bar-shaped permanent magnets is manifest as attraction if we bring two opposite poles close together (north-near-south or south-near-north) and repulsion if we bring two like poles into proximity (north-near-north or south-near-south). Either way, the force increases as the distance between the ends of the magnets decreases.
Some electromagnets produce fields so powerful that no human can pull them apart if they get “stuck” together, and no one can bring them all the way together against their mutual repulsive force. (We’ll explore how electromagnets work later in this chapter.) Industrial workers can use huge electromagnets to carry heavy pieces of scrap iron or steel from place to place. Other electromagnets can provide sufficient repulsion to suspend one object above another, an effect known as magnetic levitation.
Electric Charge Carriers in Motion
Whenever the atoms in a sample of ferromagnetic material align to any extent rather than existing in a random orientation, a magnetic field surrounds the sample. A magnetic field can also result from the motion of electric charge carriers. In a wire, electrons move in incremental “hops” along the conductor from atom to atom. In a permanent magnet, the movement of orbiting electrons occurs in such a manner that an effective current arises.
Magnetic fields can arise from the motion of charged particles through space, as well as from the motion of charge carriers through a conductor. The sun constantly ejects protons and helium nuclei, both of which carry positive electric charges. These particles produce effective currents as they travel through space. The effective currents in turn generate magnetic fields. When these fields interact with the geomagnetic field, the subatomic particles change direction and accelerate toward the geomagnetic poles.
When an eruption on the sun, called a solar flare, occurs, the sun ejects far more charged subatomic particles than usual. As these particles approach the geomagnetic poles, their magnetic fields, working together, disrupt the geomagnetic field, spawning a geomagnetic storm. Such an event causes changes in the earth’s upper atmosphere, affecting “shortwave radio” communications and producing the aurora borealis (“northern lights”) and aurora australis (“southern lights”), well-known to people who dwell at high latitudes. If a geomagnetic storm reaches sufficient intensity, it can interfere with wire communications and electric power transmission at the surface.
Lines of Flux
Physicists consider magnetic fields to comprise flux lines, or lines of flux. The intensity of the field depends on the number of flux lines passing at right angles through a region having a certain cross-sectional area, such as a centimeter squared (cm2) or a meter squared (m2). The flux lines are not actual material fibers, but their presence can be shown by means of a simple experiment.
Have you seen the classical demonstration in which iron filings lie on a sheet of paper, and then the experimenter holds a permanent magnet underneath the sheet? The filings arrange themselves in a pattern that shows, roughly, the “shape” of the magnetic field in the vicinity of the magnet. A bar magnet has a field whose lines of flux exhibit a characteristic pattern (Fig. 8-1).
8-1 Magnetic flux around a bar magnet.
Another experiment involves passing a current-carrying wire through the paper at a right angle. The iron filings bunch up in circles centered at the point where the wire passes through the paper. This experiment shows that the lines of flux around a straight, current-carrying wire form concentric circles in any plane passing through the wire at a right angle. The center of every “flux circle” lies on the wire, which constitutes the path along which the charge carriers move (Fig. 8-2).
8-2 Magnetic flux produced by charge carriers traveling in a straight line.
Polarity
A magnetic field has a specific orientation at any point in space near a current-carrying wire or a permanent magnet. The flux lines run parallel with the direction of the field. Scientists consider the magnetic field to begin, or originate, at a north pole, and to end, or terminate, at a south pole. These poles do not correspond to the geomagnetic poles; in fact, they’re the opposite! The north geomagnetic pole is in reality a south pole because it attracts the north poles of magnetic compasses. Similarly, the south geomagnetic pole is really a north pole because it attracts the south poles of compasses. In the case of a permanent magnet, we can usually (but not always) tell where the magnetic poles are located. Around a current-carrying wire, the magnetic field revolves endlessly.
A charged electric particle (such as a proton) hovering in space forms an electric monopole, and the electric flux lines around it aren’t closed. A positive charge does not have to mate with a negative charge. The electric flux lines around any stationary, charged particle run outward in all directions for a theoretically infinite distance. But magnetic fields behave according to stricter laws. Under normal circumstances, all magnetic flux lines form closed loops. In the vicinity of a magnet, we can always find a starting point (the north pole) and an ending point (the south pole). Around a current-carrying wire, the loops form circles.
Magnetic Dipoles
You might at first suppose that the magnetic field around a current-carrying wire arises from a monopole, or that no poles exist. The concentric flux circles don’t seem to originate or terminate anywhere. But you can assign originating and terminating points to those circles, thereby defining a magnetic dipole—a pair of opposite magnetic poles in close proximity.
Imagine that you hold a flat piece of paper next to a current-carrying wire, so that the wire runs along one edge of the sheet. The magnetic circles of flux surrounding the wire pass through the sheet of paper, entering one side and emerging from the other side, so you have a “virtual magnet.” Its north pole coincides with the face of the paper sheet from which the flux circles emerge. Its south pole coincides with the opposite face of the sheet, into which the flux circles plunge.
The flux lines in the vicinity of a magnetic dipole always connect the two poles. Some flux lines appear straight in a local sense, but in the larger sense they always form curves. The greatest magnetic field strength around a bar magnet occurs near the poles, where the flux lines converge or diverge. Around a current-carrying wire, the greatest field strength occurs near the wire.
Magnetic Field Strength
Physicists and engineers express the overall magnitude, or quantity, of a magnetic field in units called webers, symbolized Wb. We can employ a smaller unit, the maxwell (Mx), for weak fields. One weber equals 100,000,000 (108) maxwells. Therefore
1 Wb = 108 Mx
and
1 Mx = 10−8 Wb
The Tesla and the Gauss
If you have a permanent magnet or an electromagnet, you might see its “strength” expressed in terms of webers or maxwells. But more often, you’ll hear or read about units called teslas (T) or gauss (G). These units define the concentration, or intensity, of the magnetic field as its flux lines pass at right angles through flat regions having specific cross-sectional areas.
The flux density, or number of “flux lines per unit of cross-sectional area,” forms a more useful expression for magnetic effects than the overall quantity of magnetism. In equations, we denote flux density using the letter B. A flux density of one tesla equals one weber per meter squared (1 Wb/m2). A flux density of one gauss equals one maxwell per centimeter squared (1 Mx/cm2). As things work out, the gauss equals 0.0001 (10−4) tesla, so we have the relations
1 G = 10−4 T
and
1 T = 104 G
If you want to convert from teslas to gauss (not gausses!), multiply by 104. If you want to convert from gauss to teslas, multiply by 10−4.
Quantity versus Density
If the distinctions between webers and teslas, or between maxwells and gauss, confuse you, think of an ordinary light bulb. Suppose that a lamp emits 15 W of visible-light power. If you enclose the bulb completely, then 15 W of visible light strike the interior walls of the chamber, regardless of the size of the chamber. But this notion doesn’t give you a useful notion of the brightness of the light. You know that a single bulb produces plenty of light if you want to illuminate a closet, but nowhere near enough light to illuminate a gymnasium. The important consideration is the number of watts per unit of area. When you say that a bulb gives off so-many watts of light overall, it’s like saying that a magnet has a magnetic quantity of so-many webers or maxwells. When you say that the bulb produces so-many watts of light per unit of area, it’s like saying that a magnetic field has a flux density of so-many teslas or gauss.
Magnetomotive Force
When we work with wire loops, solenoidal (helical) coils, and rod-shaped electromagnets, we can quantify a phenomenon called magnetomotive force with a unit called the ampere-turn (At). This unit describes itself well: the number of amperes flowing in a coil or loop, times the number of turns that the coil or loop contains.
If we bend a length of wire into a loop and drive 1 A of current through it, we get 1 At of magnetomotive force inside the loop. If we wind the same length of wire (or any other length) into a 50-turn coil and keep driving 1 A of current through it, the resulting magnetomotive force increases by a factor of 50, to 50 At. If we then reduce the current in the 50-turn loop to 1/50 A or 20 mA, the magnetomotive force goes back down to 1 At.
Sometimes, engineers employ a unit called the gilbert to express magnetomotive force. One gilbert (1 Gb) equals approximately 0.7958 At. The gilbert represents a slightly smaller unit than the At does. Therefore, if we want to determine the number of ampere-turns when we know the number of gilberts, we should multiply by 0.7958. To determine the number of gilberts when we know the number of ampere-turns, we should multiply by 1.257.
Magnetomotive force does not depend on core material or loop diameter. Even if we place a metal rod in a solenoidal coil, the magnetomotive force will not change if the current through the wire remains the same. A tiny 100-turn air-core coil carrying 1 A produces the same magnetomotive force as a huge 100-turn air-core coil carrying 1 A. Magnetomotive force depends only on the current and the number of turns.
Flux Density versus Current
In a straight wire carrying a steady, direct current and surrounded by air or a vacuum, we observe the greatest flux density near the wire, and diminishing flux density as we get farther away from the wire. We can use a simple formula to express magnetic flux density as a function of the current in a straight wire and the distance from the wire.
Imagine an infinitely thin, absolutely straight, infinitely long length of wire (that’s the ideal case). Suppose that the wire carries a current of I amperes. Represent the flux density (in teslas) as B. Consider a point P at a distance r (in meters) from the wire, measured in a plane perpendicular to the wire, as shown in Fig. 8-3. We can find the flux density at point P using the formula
B = 2 × 10−7I/r
8-3 The magnetic flux density varies inversely with the distance from a wire carrying constant current.
We can consider the value of the constant, 2 × 10−7, mathematically exact to any desired number of significant figures.
Of course, we’ll never encounter a wire with zero thickness or infinite length. But as long as the wire thickness constitutes a small fraction of r, and as long as the wire is reasonably straight near point P, this formula works quite well in most applications.
What is the flux density Bt in teslas at a distance of 200 mm from a straight, thin wire carrying 400 mA of DC?
Solution
First, we must convert all quantities to units in the International System (SI). Thus, we have r = 0.200 m and I = 0.400 A. We can input these values directly into the formula for flux density to obtain
Bt = 2.00 × 10−7 × 0.400/0.200 = 4.00 × 10−7 T
Problem 8-2
In the above-described scenario, what is the flux density Bg (in gauss) at point P?
Solution
To figure this out, we must convert from teslas to gauss, multiplying the result in the solution to Problem 8-1 by 104 to get
Bg = 4.00 × 10−7 × 104 = 4.00 × 10−3 G
Electromagnets
The motion of electrical charge carriers always produces a magnetic field. This field can reach considerable intensity in a tightly coiled wire having many turns and carrying a large current. When we place a ferromagnetic rod called a core inside a coil, as shown in Fig. 8-4, the magnetic lines of flux concentrate in the core, and we have an electromagnet. Most electromagnets have cylindrical cores. The length-to-radius ratio can vary from extremely low (fat pellet) to extremely high (thin rod). Regardless of the length-to-radius ratio, the flux produced by current in the wire temporarily magnetizes the core.
8-4 A simple electromagnet.
Direct-Current Types
You can build a DC electromagnet by wrapping a couple of hundred turns of insulated wire around a large iron bolt or nail. You can find these items in any good hardware store. You should test the bolt for ferromagnetic properties while you’re still in the store, if possible. (If a permanent magnet “sticks” to the bolt, then the bolt is ferromagnetic.) Ideally, the bolt should measure at least ⅜ inch (approximately 1 cm) in diameter and at least 6 inches (roughly 15 cm) long. You must use insulated wire, preferably made of solid, soft copper.
Wind the wire at least several dozen (if not 100 or more) times around the bolt. You can layer the windings if you like, as long as they keep going around in the same direction. Secure the wire in place with electrical or masking tape. A large 6-V “lantern battery” can provide plenty of DC to operate the electromagnet. If you like, you can connect two or more such batteries in parallel to increase the current delivery. Never leave the coil connected to the battery for more than a few seconds at a time.
All DC electromagnets have defined north and south poles, just as permanent magnets have. However, an electromagnet can get much stronger than any permanent magnet. The magnetic field exists only as long as the coil carries current. When you remove the power source, the magnetic field nearly vanishes. A small amount of residual magnetism remains in the core after the current stops flowing in the coil, but this field has minimal intensity.
Alternating-Current Types
Do you suspect that you can make an electromagnet extremely powerful if, rather than using a lantern battery for the current source, you plug the ends of the coil directly into an AC utility outlet? In theory, you can do this. But don’t! You’ll expose yourself to the danger of electrocution, expose your house to the risk of electrical fire, and most likely cause a fuse or circuit breaker to open, killing power to the device anyway. Some buildings lack the proper fuses or circuit breakers to prevent excessive current from flowing through the utility wiring in case of an overload. If you want to build and test a safe AC electromagnet, my book, Electricity Experiments You Can Do at Home (McGraw-Hill, 2010), offers instructions for doing it.
Some commercially manufactured electromagnets operate from 60-Hz utility AC. These magnets “stick” to ferromagnetic objects. The polarity of the magnetic field reverses every time the direction of the current reverses, producing 120 fluctuations, or 60 complete north-to-south-to-north polarity changes, every second. In addition, the instantaneous intensity of the magnetic field varies along with the AC cycle, reaching alternating-polarity peaks at 1/120-second intervals and nulls of zero intensity at 1/120-second intervals. Any two adjacent peaks and nulls occur 1/4 cycle, or 1/240 second, apart.
If you bring a permanent magnet or DC electromagnet near either “pole” of an AC electromagnet, no net force results from the AC electromagnetism itself because equal and opposite attractive and repulsive forces occur between the alternating magnetic field and any steady external field. But the permanent magnet or the DC electromagnet attracts the core of the AC electromagnet, whether the AC device carries current or not.
Problem 8-3
Suppose that we apply 80-Hz AC to an electromagnet instead of the standard 60 Hz. What will happen to the interaction between the alternating magnetic field and a nearby permanent magnet or DC electromagnet?
Solution
Assuming that the behavior of the core material remains the same, the situation at 80 Hz will not change from the 60-Hz case. In theory, the AC frequency makes no difference in the behavior of an AC electromagnet. In practice, however, the magnetic field weakens at high AC frequencies because the AC electromagnet’s inductance tends to impede the flow of current. This so-called inductive reactance depends on the number of coil turns, and also on the characteristics of the ferromagnetic core.
Magnetic Materials
Ferromagnetic substances cause magnetic lines of flux to bunch together more tightly than they exist in free space. A few materials cause the lines of flux to dilate compared with their free-space density. We call these substances diamagnetic. Examples of such materials include wax, dry wood, bismuth, and silver. No diamagnetic material reduces the strength of a magnetic field by anywhere near the factor that ferromagnetic substances can increase it. Usually, engineers use diamagnetic objects to keep magnets physically separated while minimizing the interaction between them.
Permeability
Permeability expresses the extent to which a ferromagnetic material concentrates magnetic lines of flux relative to the flux density in a vacuum. By convention, scientists assign a permeability value of 1 to a vacuum. If we have a coil of wire with an air core and we drive DC through the wire, then the flux inside the coil is about the same as it would be in a vacuum. Therefore, the permeability of air equals almost exactly 1. (Actually it’s a tiny bit higher, but the difference rarely matters in practice.)
If we place a ferromagnetic core inside the coil, the flux density increases, sometimes by a large factor. By definition, the permeability equals that factor. For example, if a certain material causes the flux density inside a coil to increase by a factor of 60 compared with the flux density in air or a vacuum, that material has a permeability of 60. Diamagnetic materials have permeability values less than 1, but never very much less. Table 8-1 lists the permeability values for some common substances.
Table 8-1. Permeability Values for Some Common Materials
Retentivity
When we subject a substance, such as iron, to a magnetic field as intense as it can handle, say by enclosing it in a wire coil carrying high current, some residual magnetism always remains after the current stops flowing in the coil. Retentivity, also known as remanence, quantifies the extent to which a substance “memorizes” a magnetic field imposed on it.
Imagine that we wind a wire coil around a sample of ferromagnetic material and then drive so much current through the coil that the magnetic flux inside the core reaches its maximum possible density. We call this condition core saturation. We measure the flux density in this situation, and get a figure of Bmax (in teslas or gauss). Now suppose that we remove the current from the coil, and then we measure the flux density inside the core again, obtaining a figure of Brem (in teslas or gauss, as before). We can express the retentivity Br of the core material as a ratio according to the formula
Br = Brem/Bmax
or as a percentage using the formula
Br% = 100 Brem/Bmax
As an example, suppose that a metal rod can attain a flux density of 135 G when enclosed by a current-carrying coil. Imagine that 135 G represents the maximum possible flux density for that material. (For any substance, such a maximum always exists, unique to that substance; further increasing the coil current or number of turns will not magnetize it any further.) Now suppose that we remove the current from the coil, and 19 G remain in the rod. Then the retentivity Br is
Br = 19/135 = 0.14
As a percentage,
Br% = 100 × 19/135 = 14%
Certain ferromagnetic substances exhibit high retentivity, and therefore, make excellent permanent magnets. Other ferromagnetic materials have poor retentivity. They can sometimes work okay as the cores of electromagnets, but they don’t make good permanent magnets.
If a ferromagnetic substance has low retentivity, it can function as the core for an AC electromagnet because the polarity of the magnetic field in the core follows along closely as the current in the coil alternates. If the material has high retentivity, the material acts “magnetically sluggish” and has trouble following the current reversals in the coil. Substances of this sort don’t work well in AC electromagnets.
Problem 8-4
Suppose that we wind a coil of wire around a metal core to make an electromagnet. We find that by connecting a variable DC source to the coil, we can drive the magnetic flux density in the core up to 0.500 T but no higher. When we shut down the current source, the flux density inside the core drops to 500 G. What’s the retentivity of this core material?
Solution
First, let’s convert both flux density figures to the same units. We recall that 1 T = 104 G. Therefore, the flux density in gauss is 0.500 × 104 = 5,000 G when the current flows in the coil, and 500 G after we remove the current. “Plugging in” these numbers gives us the ratio
Br = 500/5,000 = 0.100
or the percentage
Br% = 100 × 500/5,000 = 100 × 0.100 = 10.0%
Permanent Magnets
Industrial engineers can make any suitably shaped sample of ferromagnetic material into a permanent magnet. The strength of the magnet depends on two factors:
• The retentivity of the material used to make it
• The amount of effort put into magnetizing it
The manufacture of powerful permanent magnets requires an alloy with high retentivity. The most “magnetizable” alloys derive from specially formulated mixtures of aluminum, nickel, and cobalt, occasionally including trace amounts of copper and titanium. Engineers place samples of the selected alloy inside heavy wire coils carrying high, continuous DC for an extended period of time.
You can magnetize any piece of iron or steel. Some technicians use magnetized tools when installing or removing screws from hard-to-reach places in computers, wireless transceivers, and other devices. If you want to magnetize a tool, stroke its metal shaft with the end of a powerful bar magnet several dozen times. But beware: Once you’ve imposed residual magnetism in a tool, it will remain magnetized to some extent forever!
Flux Density inside a Long Coil
Consider a long, helical coil of wire, commonly known as a solenoid, having n turns in a single layer. Suppose that it measures s meters in length, carries a steady direct current of I amperes, and has a ferromagnetic core of permeability μ. Assuming that the core has not reached a state of saturation, we can calculate the flux density Bt (in teslas) inside the material using the formula
Bt = 4π × 10−7 μnI/s ≈ 1.2566 × 10−6 μnI/s
If we want to calculate the flux density Bg (in gauss), we can use the formula
Bg = 4π × 10−3 μnI/s ≈ 0.012566 μnI/s
Problem 8-5
Imagine a DC electromagnet that carries a certain current. It measures 20 cm long, and has 100 turns of wire. The core, which has permeability μ = 100, has not reached a state of saturation. We measure the flux density inside it as Bg = 20 G. How much current flows in the coil?
Solution
Let’s start by ensuring that we use the proper units in our calculation. We’re told that the electromagnet measures 20 cm in length, so we can set s = 0.20 m. The flux density equals 20 G. Using algebra, we can rearrange the second of the above formulas so that it solves for I. We start with
Bg = 0.012566 μnI/s
Dividing through by I, we get
Bg/I = 0.012566 μn/s
When we divide both sides by Bg, we obtain
I−1 = 0.012566 μn/(sBg)
Finally, we take the reciprocal of both sides to get
I = 79.580 sBg/(μn)
Now we can input the numbers from the statement of the problem. We calculate
I = 79.580 sBg/(μn) = 79.580 × 0.20 × 20/(100 × 100)
= 79.580 × 4.0 × 10−4 = 0.031832 A = 31.832 mA
We should round this result off to 32 mA.
Magnetic Machines
Electrical relays, bell ringers, electric “hammers,” and other mechanical devices make use of the principle of the solenoid. Sophisticated electromagnets, sometimes in conjunction with permanent magnets, allow us to construct motors, meters, generators, and other electromechanical devices.
The Chime
Figure 8-5 illustrates a bell ringer, also known as a chime. Its solenoid comprises an electromagnet. The ferromagnetic core has a hollow region in the center along its axis, through which a steel rod, called the hammer, passes. The coil has many turns of wire, so the electromagnet produces a high flux density if a substantial current passes through the coil.
8-5 A bell ringer, also known as a chime.
When no current flows in the coil, gravity holds the rod down so that it rests on the plastic base plate. When a pulse of current passes through the coil, the rod moves upward at high speed. The magnetic field “wants” the ends of the rod, which has the same length as the core, to align with the ends of the core. But the rod’s upward momentum causes it to pass through the core and strike the ringer. Then the steel rod falls back to its resting position, allowing the ringer to reverberate.
The Relay
We can’t always locate switches near the devices they control. For example, suppose that you want to switch a communications system between two different antennas from a station control point 50 meters away. Wireless antenna systems carry high-frequency AC (the radio signals) that must remain within certain parts of the circuit. A relay makes use of a solenoid to allow remote-control switching.
Figure 8-6A illustrates a simple relay, and Fig. 8-6B shows the schematic diagram for the same device. A movable lever, called the armature, is held to one side (upward in this diagram) by a spring when no current flows through the coil. Under these conditions, terminal X contacts terminal Y, but X does not contact Z. When a sufficient current flows in the coil, the armature moves to the other side (downward in this illustration), disconnecting terminal X from terminal Y, and connecting X to Z.
8-6 Simplified drawing of a relay (at A) and the schematic symbol for the same relay (at B).
A normally closed relay completes the circuit when no current flows in the coil, and breaks the circuit when coil current flows. (“Normal,” in this sense, means the absence of coil current.) A normally open relay does the opposite, completing the circuit when coil current flows, and breaking the circuit when coil current does not flow. The relay shown in Fig. 8-6 can function either as a normally open relay or a normally closed relay, depending on which contacts we select. It can also switch a single line between two different circuits.
These days, engineers install relays primarily in circuits and systems that must handle large currents or voltages. In applications in which the currents and voltages remain low to moderate, electronic semiconductor switches, which have no moving parts, offer better performance and reliability than relays.
The DC Motor
Magnetic fields can produce considerable mechanical forces. We can harness these forces to perform useful work. A DC motor converts DC into rotating mechanical energy. In this sense, a DC motor constitutes a specialized electromechanical transducer. Such devices range in size from nanoscale (smaller than a bacterium) to megascale (larger than a house). Nanoscale motors can circulate in the human bloodstream or modify the behavior of internal body organs. Megascale motors can pull trains along tracks at hundreds of kilometers per hour.
In a DC motor, we connect a source of electricity to a set of coils, producing magnetic fields. The attraction of opposite poles, and the repulsion of like poles, is switched in such a way that a constant torque (rotational force) results. As the coil current increases, so does the torque that the motor can produce—and so does the energy it takes to operate the motor at a constant speed.
Figure 8-7 illustrates a DC motor in simplified form. The armature coil rotates along with the motor shaft. A set of two coils called the field coil remains stationary. Some motors use a pair of permanent magnets instead of a field coil. Every time the shaft completes half a rotation, the commutator reverses the current direction in the armature coil, so the shaft torque continues in the same angular direction. The shaft’s angular (rotational) momentum carries it around so that it doesn’t “freeze up” at the points in time when the current reverses direction.
8-7 Simplified drawing of a DC motor.
Electric Generator
The construction of an electric generator resembles that of an electric motor, although the two devices function in the opposite sense. We might call a generator a specialized mechano-electrical transducer (although I’ve never heard anybody use that term). Some generators can also operate as motors; we call such devices motor-generators.
A typical generator produces AC when a coil rotates in a strong magnetic field. We can drive the shaft with a gasoline-powered motor, a turbine, or some other source of mechanical energy. Some generators employ commutators to produce pulsating DC output, which we can filter to obtain pure DC for use with precision equipment.
Quiz
Refer to the text in this chapter if necessary. A good score is 18 correct. Answers are in the back of the book.
1. If a solenoidal wire coil has 50 turns and carries 500 mA, then it gives rise to a magnetomotive force of
(a) 25 At.
(b) 50 At.
(c) 500 At.
(d) None of the above
2. The magnetic field produced by an electromagnet connected to a lantern battery
(a) fluctuates in intensity from instant to instant in time, and periodically reverses polarity.
(b) fluctuates in intensity from instant to instant in time, but maintains the same polarity at all times.
(c) maintains constant intensity but periodically reverses polarity.
(d) maintains constant intensity and the same polarity all the time.
3. A sample of ferromagnetic material
(a) cannot work as the core for an electromagnet.
(b) does not “attract” or “stick to” magnets.
(c) causes magnetic flux lines to bunch up more tightly than they do in free space.
(d) has a permeability of 0.
4. The magnetic flux contours near the ends of a bar magnet take the form of
(a) straight lines parallel to the bar’s axis.
(b) straight lines perpendicular to the bar’s axis.
(c) circles whose centers lie on the bar’s axis.
(d) curves that converge on (or diverge from) the bar’s ends.
5. If you want to build an electromagnet that will produce an alternating magnetic field when you connect it to a lantern battery, you should choose a core material that has
(a) high permeability and high retentivity.
(b) high permeability and low retentivity.
(c) low permeability and high retentivity.
(d) no known characteristics; you can’t build such an electromagnet.
6. A metal rod can support a flux density of up to 800 G when DC flows in a coil surrounding it. When you remove the rod leaving only air, the flux density in that air goes down to 20 G. What’s the permeability of the rod?
(a) You need more information to figure it out.
(b) 40
(c) 0.025
(d) 410
7. What’s the retentivity of the rod described in Question 6?
(a) You need more information to figure it out.
(b) 40
(c) 0.025
(d) 410
8. Which of the following units expresses magnetic flux density?
(a) Tesla
(b) Ampere
(c) Coulomb
(d) Siemens
9. What’s the magnetic flux density at a point 2.00 m away from a straight, thin wire carrying 600 mA of DC?
(a) 6.00 × 10−7 T
(b) 6.00 × 10−8 T
(c) 3.00 × 10−7 T
(d) 3.00 × 10−8 T
10. You wind 70 turns of heavy copper insulated wire in a coil around a rod-shaped ferromagnetic core. You drive 22 A of DC through the coil. Then you double the current to 44 A. If the core reaches a state of saturation and if 3.3 A or more flows through the coil, the current increase described here causes the flux density inside the core to essentially
(a) stay the same.
(b) increase by a factor of the square root of 2.
(c) double.
(d) quadruple.
11. A normally open relay completes an external circuit
(a) whether current flows in its coil or not.
(b) only when current flows in its coil.
(c) only when no current flows in its coil.
(d) only when AC flows in its coil.
12. At a specific point on the earth’s surface, the term geomagnetic declination refers to
(a) the vertical tilt of the earth’s magnetic flux lines.
(b) the horizontal deflection of the earth’s magnetic field.
(c) the geomagnetic flux density through a horizontal plane.
(d) the angular difference between geomagnetic north and true north.
13. If you want to make a powerful permanent magnet, you’ll need an alloy that has
(a) low permeability.
(b) high density.
(c) high retentivity.
(d) low resistance per unit of length.
14. When you place a current-carrying wire coil in a vacuum, the magnetic flux density inside that coil
(a) goes down to zero.
(b) increases compared with the flux density when it has a ferromagnetic core.
(c) decreases compared with the flux density when it has a ferromagnetic core.
(d) remains the same as the flux density when it has a ferromagnetic core.
15. At the geomagnetic equator, the geomagnetic field’s force on a compass needle is
(a) horizontal.
(b) vertical.
(c) slanted.
(d) nonexistent.
16. If a solenoidal wire coil has 1000 turns and carries 30.00 mA of DC, then its magnetomotive force is
(a) dependent on the coil’s length, diameter, and core material.
(b) 37.71 Gb.
(c) 1131 Gb.
(d) 6.885 Gb.
17. If a solenoidal coil has 60 turns and you connect it to a 6.3-V lantern battery, how much magnetomotive force does that coil produce?
(a) It depends on its diameter.
(b) It depends on its DC conductance.
(c) It depends on its core material.
(d) All of the above
18. If you insert a ferromagnetic rod of permeability 16.0 inside the coil described in Question 17, the magnetomotive force will
(a) increase by a factor of 4.00.
(b) increase by a factor of 16.0.
(c) increase by a factor of 256.
(d) not change.
19. The magnetic force between the ends of two electromagnets depends on
(a) the electromagnets’ core material.
(b) the distance between those ends.
(c) the currents in the coils.
(d) All of the above
20. Geomagnetic storms often accompany
(a) “northern lights” (aurora borealis).
(b) sudden changes in the sun’s diameter.
(c) polarity reversals in the earth’s magnetic field.
(d) thundershowers in their immediate vicinity.