* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Electromagnetic Induction
Magnetic field wikipedia , lookup
Earthing system wikipedia , lookup
National Electrical Code wikipedia , lookup
Three-phase electric power wikipedia , lookup
Wireless power transfer wikipedia , lookup
Insulator (electricity) wikipedia , lookup
Electromagnetism wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Multiferroics wikipedia , lookup
Electrical resistance and conductance wikipedia , lookup
Magnetoreception wikipedia , lookup
Magnetochemistry wikipedia , lookup
Electricity wikipedia , lookup
Force between magnets wikipedia , lookup
High voltage wikipedia , lookup
Magnetohydrodynamics wikipedia , lookup
Superconductivity wikipedia , lookup
Hall effect wikipedia , lookup
History of electrochemistry wikipedia , lookup
Friction-plate electromagnetic couplings wikipedia , lookup
Magnetic core wikipedia , lookup
Electric current wikipedia , lookup
Induction heater wikipedia , lookup
Electrical injury wikipedia , lookup
Lorentz force wikipedia , lookup
Electric machine wikipedia , lookup
Eddy current wikipedia , lookup
Superconducting magnet wikipedia , lookup
Scanning SQUID microscope wikipedia , lookup
Electromagnet wikipedia , lookup
Alternating current wikipedia , lookup
CHAPTER· 25 Electromagnetic Induction ... . ... . .... .... . ... . Chapter Outline ~ Go With the Flow Aluminum is classified as a non-magnetic substance. Two aluminum rings, one with a slit and one a continuous ring, are placed over a magnetic field generator that is producing a constantly-changing magnetic field. Why does one ring float but the other one does not? 25.1 CREATING ELECTRIC CURRENT FROM CHANGING MAGNETIC FIELDS · · · · Faraday's Discovery Electromotive Force Electric Generators Alternating Current Generator 25.2 EFFECTS OF CHANGING MAGNETIC FIELDS: INDUCED EMF · Lenz's Law · Self-Inductance · Transformers • VConcept Check L evitation? There is no superconductor or permanent magnet in this photograph. The ring is made of aluminum, a non-magnetic conductor. The coil of wire around the central rod produces a continually changing magnetic field. You may never have seen such a floating ring, but the physical principle that explains why it is levitated also explains how the modern electrical distribution system works. The following terms or concepts from earl ier chapters are important for a good understanding of this chapter. If you are not familiar with them, you should review them before studying this chapter. . potential difference, electron pump, current, resistance, Chapter 22 . right-hand rules, electric motor, Chapter 24 515 - 25.1 Objectives · explain how a changing magnetic field produces an electric current. · define EMF; show an ability to calculate EMF of wires moving in a magnetic field and know the limitations of the equation. · explain how an electric generator works and how it differs from a motor. · explain the difference between peak and effective voltage and current; use both in solving problems. To induce current, there must be relative motion of a wire and the magnetic field. F. Y. I. Michael Faraday left school at age 14 to become an apprentice to a bookbinder. He read most of the books in the shop. Joseph Henry left school at age 13 to work for a watch maker. Later in life, Faraday became director of the Royal Institution in London, founded by the American Benjamin Thomson (Count Rumford). Henry became the director of the Smithsonian Institution in Washington DC, founded by the Englishman James Smithson. FIGURE 25-1. When a wire is moved in a magnetic field, an electric current flows in the wire, but only while the wire is moving. The direction of the current flow depends on the direction the wire is moving through the field. The arrows indicate the direction of conventional current flow. 516 Electromagnetic Induction .......................................... CREATING ELECTRIC CURRENT FROM CHANGING MAGNETIC FIELDS I n 1822, Michael Faraday wrote a goal in his notebook: "Convert Magnetism into Electricity." After nearly ten years of unsuccessful experiments, he was able to show that a changing magnetic field could produce electric current. In the same year, Joseph Henry, an American high school teacher, made the same discovery. Faraday's Discovery Oersted had discovered that an electric current produces a magnetic field. Faraday tried all combinations of field and wire without success until he found he could induce current by moving the wire in a magnetic field. Figure 25-1 shows one of Faraday's experiments. A wire loop that is part of a closed circuit is placed in a magnetic field. If the wire moves up through the field, the current moves in one direction. When the wire moves down through the field, the current moves in the opposite direction. If the wire is held stationary or is moved parallel to the field, no current flows. An electric current is generated in a wire only when the wire cuts magnetic field lines. To generate current, either the conductor can move through a magnetic field, or the magnetic field can move past a conductor. It is the relative motion between the wire and the magnetic field that produces the current. The process of generating a current through a circuit in this way is called electromagnetic induction. In what direction does the current move? To find the force on the charges in the wire, use the third right-hand rule described in Chapter 24. Hold your right hand so that your thumb points in the direction in which the wire is moving and your fingers point in the direction of the magnetic field. The palm of your hand will point in the direction of the conventional (positive) current flow, Figure 25-2. Wire moving up ( Current FIGURE 25-2. The right-hand rule can be used to find the direction of the forces on the charges in a conductor that is moving in a magnetic field. B F s ~/IB_V_ N Motion of the wire v •• Electromotive Force When we studied electric circuits, we learned that a charge pump is needed to produce a continuous current flow. The potential increase, or voltage, given to the charges by the pump is called the electromotive force, or EMF. Electromotive force, however, is not a force; it is a potential increase and is measured in volts. Thus the term EMF is misleading. Like many other historical terms still in use, it originated before electricity was well understood. What creates the increase in potential that can cause an induced current to flow? When a wire is moved through a magnetic field, a force acts on the charges and they move in the direction of the force. Work is done on the charges. Their electrical potential energy, and thus their potential, is increased. The increase in potential is called the induced EMF. The EMF, measured in volts, depends on the magnetic field strength, B, the length of the wire in the magnetic field, L, and the velocity of the wire in the field, v. If B, v, and the direction of the length of the wire are mutually perpendicular, I EMF = Electromotive volts. force is measured The EMF depends on magnetic field strength, the length of the Wire, and its velocity perpendicular to the field. Coil s BLv·1 If the moving wire is part of a closed circuit, the EMF will cause a current to flow in the circuit in the direction of the EMF. If a wire moves through a magnetic field at an angle to the field, only the component of the wire's velocity that is perpendicular to the direction of the field generates EMF. A microphone is a simple application that depends on an induced EMF. The "dynamic" microphone is similar in construction to a loudspeaker. The microphone in Figure 25-3 has a diaphragm attached to a coil of wire that is free to move in a magnetic field. Sound waves vibrate the diaphragm, which moves the coil in the magnetic field. The motion of the coil, in turn, induces an EMF across the ends of the coil. The voltage generated is small, typically 10-3 V, but it can be increased, or amplified, by electronic devices. 25.1 Creating Electric Current Magnet (also serves as the supporting frame) .~ Connectlng Air vent wires FIGURE 25-3. Schematic of a moving coil microphone. The aluminum diaphragm is connected to a coil in a magnetic field. When sound waves vibrate the diaphragm, the coil moves in the magnetic field, generating a current proportional to the sound wave. from Changing Magnetic Fields 517 POCKET LAB MAKING CURRENTS Hook the ends of a 1 m length of wire to the binding posts of a galvanometer (or microammeter). Make several overlapping loops in the wire. Watch the readings on the wire as you move a pair of neodymiummagnets (or a strong horseshoe magnet) near the loops. Record your observations.What can you do to increase the current? Replace the 1 m length of wire with a pre-formed coil and see how much current you can produce. Describeyour results. Example Problem Induced EMF A straight wire 0.20 m long moves perpendicularly through a magnetic field of magnetic induction 8.0 x 10-2 T at a speed of 7.0 m/s. a. What EMF is induced in the wire? b. The wire is part of a circuit that has a resistance of 0.50 D. What current flows in the circuit? Given: L = 8 = 0.20 m 8.0 X 10-2 T v = 7.0 mls R = 0.500 Unknowns: a. EMF b. I Basicequations: a. EMF = 8Lv b. I = VIR Solution: a. EMF = = EMF b. I = 8Lv (8.0 x 10-2 T)(0.20 m)(7.0 m/s) (8.0 x 10-2 N/A·m)(0.20 m)(7.0 m/s) = 0.11 (_N_)(m)(m) A'm = ~ = R 0.11 V 0.500 s = 0.11 W = 0.11 V A 0.22 A Practice Problems 1. A straight wire, 0.5 m long, is moved straight up through a O.4-T magnetic field pointed in the horizontal direction at a speed of 20 m/s. a. What EMF is induced in the wire? b. The wire is part of a circuit of total resistance of 6.0 D. What is the current in the circuit? 2. A straight wire, 25 m long, is mounted on an airplane flying at 125 m/s. The wire moves perpendicularly through Earth's magnetic field (8 = 5.0 x 10-5 T). What EMF is induced in the wire? 3. A permanent horseshoe magnet is mounted so that the magnetic field lines are vertical. If a student passesa straight wire between the poles and pulls it toward herself, the current flow through the wire is from right to left. Which is the N-pole of the magnet? ~ 4. A straight wire, 30.0 m long, moves at 2.0 mls perpendicularly through a 1.0-T magnetic field. a. What EMF is induced in the wire? b. The total resistance of the circuit of which the wire is a part is 15.0 D. What is the current? Electric Generators The electric generator, invented by Michael Faraday, converts mechanical energy to electric energy. An electric generator consists of a number of wire loops placed in a strong magnetic field. The wire is wound around an iron form to increase the strength of the field. The iron and wires are called the armature, similar to that of an electric motor. 518 Electromagnetic Induction FIGURE 25-4. 2 N 4 a An electric current is generated in a wire loop as the loop rotates (a). The cross-sectional view (b) shows the position of the loop when maximum current is generated. The numbered positions correspond to the numbered points on the graph in Figure 25-5. 1=0 b The armature is mounted so that it can rotate freely in the field. As the armature turns, the wire loops cut through the magnetic field lines, inducing an EMF. The EMF, commonly called the voltage, developed by the generator depends on the magnetic induction, B, the length of wire rotating in the field, L, and v, the speed of the loops perpendicular to the magnetic field. Increasing the number of loops in the armature increases the wire length, L, increasing the induced EMF. When a generator is connected in a closed circuit, current flows that is proportional to the induced EMF. Figure 25-4 shows a single loop generator. The direction of the induced current can be found from the third right-hand rule. As the loop rotates, the strength and direction of the current change. The current is greatest when the component of the loop's velocity perpendicular to the field is largest. This occurs when the motion of the loop is perpendicular to the magnetic field-when the loop is in the horizontal position. As the loop rotates from the horizontal to the vertical position, it moves through the magnetic field lines at an ever-increasing angle and current decreases. When the loop is in the vertical position, the wire segments move parallel to the field and the current is zero. As the loop continues to turn, the segment that was moving up begins to move down, reversing the direction of the current in the loop. This change in direction takes place each time the loop turns through 180°. The current changes smoothly from zero to some maximum value and back to zero during each half-turn of the loop. Then it reverses direction. The graph of current versus time is shown in Figure 25-5. The strength and direction of the induced current change as the armature rotates. FIGURE 25-5. This graph shows the variation of current with time as the loop in Figure 25-4b rotates. The variation of EMF with time is given by a similar graph. 25.1 Creating Electric Current from Changing Magnetic Fields 519 FIGURE 25-6. Alternating current generators transmit current to an external circuit by way of a brushslip-ring arrangement (a). The alternating current varies with time (b). i: o JL---\.---I---\--f- -/max Brushes a b Generators and motors are almost identical in construction but convert energy in opposite directions. A generator converts mechanical energy to electric energy while a motor converts electric energy to mechanical energy. In a generator, mechanical energy turns an armature in a magnetic field. The induced voltage causes current to flow. In a motor, a voltage is placed across an armature coil in a magnetic field. The voltage causes current to flow in the coil and the armature turns, producing mechanical energy from electrical energy. The direction of current produced by generators in electric utility companies alternates from one direction to the other and back 60 times each second. HELP WANTED ELECTRICIAN Electrical contractor needs electricians who have successfully completed a 5-year apprenticeship program conducted by a union or professional builder'S association. You must be a high school grad, be in good physical condition, have excellent dexterity and color vision, and be willing to work when and where there is work. You will do all aspects of the job, including reading blueprints, dealing with all types of wires, conduits, and equipment. Safety and quality work must be your highest priori' . . ct: nternational Brotherhood of Electrical Workers, 1125 15th Street, .w., Washington, DC 20005 520 Electromagnetic Induction Alternating Current Generator An energy source turns the armature of a generator in a magnetic field at a fixed number of revolutions per second. In the United States, electric utilities use a 60-Hz frequency. The current goes from one direction, to the other, and back to the first, 60 times a second. Figure 25-6 shows how an alternating current in an armature is transmitted to the rest of the circuit. The brush-slip-ring arrangement permits the armature to turn freely while still allowing the current to pass into the external circuit. As the armature turns, the alternating current varies between some maximum value and zero. If the armature is turning rapidly, the light in the circuit does not appear to dim or brighten because the changes are too fast for the eye to detect. The power produced by a generator is the product of the current and the voltage. Power is always positive because either / and V are both positive or both negative. Because / and V vary, however, the power associated with an alternating current varies and its average value is less than the power suppl ied by a direct current with the same /max and VrnaxIn fact, the average AC power is PAC =1/2P ACmax = 1/2PDC' It is common to describe alternating currents and voltages in terms of effective currents and voltages. Recall that P = /2R. Thus, the average AC power can be written in terms of the effective current, PAC = PeffR. PAC = PeffR = 1i2PDc 1i2(p maxlR F. Y. I. Jeff = y1/2J2max Jeff = 0.707Jmax Veff = 0.707Vmax The voltage generally available at wall outlets is described as 120 V, where 120 is the magnitude of the effective voltage, not the maximum voltage. Example Problem Effective Voltage and Effective Current An AC generator develops a maximum voltage of 34 V and delivers a maximum current of 0.17 A to a circuit. a. What is the effective voltage of the generator? b. What effective current is delivered to the circuit? c. What is the resistance of the circuit? Given: Vmax= 34 V Jmax= 0.17 A In an incandescent bulb, the filament temperature cannot change fast enough to keep up with the changing voltage. However, a fluorescent lamp can. Look at the blades of a fan in the light of a fluorescent lamp. You will see blue-looking blades from the 120-Hz blue flashes of excited mercury vapor. The overall yellowish light is from the phosphors on the inner surface of the tube, which emit a more slowly changing light. Unknowns: a. Veffb. Jeffc. R Basic equations: a. Veff = 0.707 Vmax b. Jefl = 0.707 Jmax c. R = Vefl Jefl Solution: a. Veff = o. 707(V max) = 0.707(34 V) = 24 V b. Jeff= 0.707(1max) = 0.707(0.17 A) = 0.12 A Veff 24 V c R = = -= 2000= • Jeff 0.12 A 2.0 X 1020 Practice Problems 5. A generator in a power plant develops a maximum voltage of 170 V. a. What is the effective voltage? b. A 60-W light bulb is placed across the generator. A maximum current of 0.70 A flows through the bulb. What effective current flows through the bulb? c. What is the resistance of the light bulb when it is working? 6. The effective voltage of a particular AC household outlet is 117 V. a. What is the maximum voltage across a lamp connected to the outlet? b. The effective current through the lamp is 5.5 A. What is the maximum current in the lamp? 7. An AC generator delivers a peak voltage of 425 V. a. What is the effective voltage in a circuit placed across the generator? b. The resistance of the circuit is 5.0 x 102 O. What is the effective current? ~ 8. If the average power dissipated by an electric light is 100 W, what is the peak power? 25.1 POCKET LAB MOTOR AND GENERATOR Make a series circuit with a Genecon (or efficient DC motor), a miniature lamp, and ammeter. Rotate the handle (or motor shaft) to try to light the lamp. Describe your results. Predict what might happen if you connect your Genecon to the Genecon from another lab group and crank yours. Try it. Describe what happens. Can more than two be connected? Creating Electric Current from Changing Magnetic Fields 521 PHYSICSLABo : The Pick Up Purpose To investigate changing magnetic fields with a telephone pickup coil. Materials · telephone pickup coil (Radio Shack #44-533 similar) · mini audio amplifier (Radio Shack #277-1008 similar) · strong permanent magnet · iron or air core solenoid coil · 9-V battery · low-voltage AC power supply · battery-powered car · 1 meter of string · masking tape or or Procedure 1. Put the 9-V battery into the amplifier and plug in the telephone pickup coil. 2. Place the strong permanent magnet on the table. Slowly bring the pickup coil near the magnet. 3. Use the suction cup to stick the pickup coil on the table. Attach the magnet to a string so that it hangs just above the pickup coil. 4. Swing the magnet like a pendulum. Twist the string so that as it untwists it will spin the magnet. 5. Attach the low-voltage AC power supply to the solenoid coil. Turn the power supply to about 2-3 V. 6. Hold the pickup coil near the solenoid coil to find where the sound is loudest. Listen to the amplifier as the pickup coil is rotated. Observations and Data 1. When does the pickup coil and amplifier make a sound in Procedure 2-4? 2. Describe the sound as the pickup coil and amplifier approaches the solenoid coil. Analysis 1. The pickup coil produces no signal when it is held stationary near the permanent magnet. Explain this. 2. Explain why rotating the pickup coil (Procedure 6) changes the loudness of the signal. 3. Predict the sound that you would hear if the solenoid coil was connected to a battery. Explain your prediction. Mini audio amplifier Applications Pickup coil 522 Electromagnetic Induction 1. Turn the battery-powered car on low speed and bring the pickup coil near to "hear" the changing magnetic fields. Predict how the sound will be different when the battery-powered car is on high speed. Try it. What happened? Why? ........................ CONCEPT REVIEW 1.1 Could you make a generator by mounting permanent magnets on the rotating shaft and having the coil stationary? Explain. 1.2 A bike generator lights the headlamp. What is the source of the energy for the bulb when the rider travels along a flat road? 1.3 Consider the microphone shown in Figure 25-3. When the diaphragm is pushed in, what is the direction of the current in the coil? 1.4 Critical Thinking: A student asks: "Why doesn't AC dissipate any power? The energy going into the lamp when the current is positive is removed when the current is negative. The net is zero." Explain why this argument is wrong . 25.2 ....................................... EFFECTS OF CHANGING MAGNETIC FIELDS: INDUCED Objectives · state Lenz's law; explain back-EMF and how it affects the operation of motors and generators. · explain the nature of selfinductance and its effects in circuits. · describe the transformer; explain the connection of turns ratio to voltage ratio; solve transformer EMF na generator, current flows when the armature turns through a magnetic field. We learned in Chapter 24 that when current flows through a wire in a magnetic field, a force is exerted on the wire. Thus, a force is exerted on the wires in the armature. In a sense, then, a generator is, at the same time, a motor. I problems. Lenis Law In what direction is the force on the wires of the armature? The direction of the force on the wires opposes the original motion of the wires. That is, the force acts to slow down the rotation of the armature. The direction of the force was first determined in 1834 by H. F. E. Lenz and is called Lenz's law. Lenz's law states: The direction of the induced current is such that According to Lenz's law, the direction of the induced current is such that the current's magnetic effects oppose the changes that produced the current. the magnetic field resulting from the induced current opposes the change in the field that caused the induced current. Note that it is the change in the field and not the field itself that is opposed by the induced FIGURE 25-7. The magnet approaching the coil causes an induced current to flow. Lenz's law predicts the direction of flow shown. magnetic effects. Figure 25-7 is a simple example of how Lenz's law works. The Npole of a magnet is moved toward the right end of a coil. To oppose the approach of the N-pole, the right end of the coil must also become N 25.2 s Effects of Changing Magnetic Fields: Induced EMF 523 POCKET LAB SLOW MAGNETS Lay the 1 m length of copper tube on the lab table. Try to pull the copper with a pair of neodymium magnets. Can you feel any force on the copper? Hold the tube by one end so that it hangs straight down. Drop a small steel marble through the tube. Use a stopwatch to measure the time needed for the marble and then for the pair of magnetsto fall through the tube. Catch the magnets in your hand. If they hit the table or floor they will break. Devise a hypothesis that would explain the strange behavior and suggest a method of testing your hypothesis. FIGURE 25-8. Sensitive balances use eddy current damping to control oscillations of the balance beam (a). As the metal plate on the end of the beam moves through the magnetic field, a current is generated in the metal. This current, in turn, produces a magnetic field that opposes the motion that caused it, and the motion of the beam is dampened (b). > Pivot 524 .;...-~"""" Electromagnetic Induction an N-pole. In other words, the magnetic field lines must emerge from the right end of the coil. Use the second right-hand rule you learned in Chapter 24. You will see that if Lenz's law is correct, the induced current must flow in a counterclockwise direction. Experiments have shown that this is so. If the magnet is turned so an S-pole approaches the coil, the induced current will be in a clockwise direction. If a generator produces only a small current, then the opposing force on the armature will be small, and the armature will be easy to turn. If the generator produces a larger current, the force on the larger current will be larger, and the armature will be more difficult to turn. A generator supplying a large current is producing a large amount of electrical energy. The opposing force on the armature means that an armature of mechanical energy must be supplied to the generator to produce the electrical energy, consistent with the law of conservation of energy. Lenz's law also applies to motors. When a current-carrying wire moves in a magnetic field, an EMF is generated. This EMF, called the back-EMF, is in a direction that opposes the current flow. When a motor is first turned on, a large current flows because of the low resistance of the motor. As the motor begins to turn, the motion of the wires across the magnetic field induces the back-EMF that opposes the current flow. Therefore, the net current flowing through the motor is reduced. If a mechanical load is placed on the motor, slowing it down, the backEMF is reduced and more current flows. If the load stops the motor, current flow can be so high that wires overheat. The heavy current required when a motor is started can cause voltage drops across the resistance of the wires that carry current to the motor. The voltage drop across the wires reduces the voltage across the motor. If a second device, such as a light bulb, is near the motor in a parallel circuit with it, the voltage at the bulb will also drop when the motor is started. The bulb will dim. As the motor picks up speed, the voltage will rise again and the bulb will brighten. When the current to the motor is interrupted by turning off a switch in the circuit or by pulling the motor's plug from a wall outlet, the sudden change in the magnetic field generates a back-EMF that can be large enough to cause a spark across the switch or between the plug and the wall outlet. A sensitive balance, Figure 25-8, such as the kind used in chemistry laboratories, uses Lenz's law to stop its oscillation when an object is placed on the pan. A piece of metal attached to the balance arm is Wire coil Wire coil Wire coil Wire coil located between the poles of a horseshoe magnet. When the balance arm swings, the metal moves through the magnetic field. Currents, called eddy-currents, are generated in the metal. These currents produce a magnetic field that acts to oppose the motion that caused the currents. Thus the metal piece is slowed down. The force opposes the motion of the metal in either direction, but does not act if the metal is still. Thus it does not change the mass read by the balance. This effect ~ is called "eddy-current damping." The magnetic field caused by the induced EMF causes the ring in the chapter-opening photo to float. The coil is driven by AC, so the magnetic field is constantly changing, and this change induces an EMF in the ring. The resulting ring current produces a magnetic field that opposes the change in the generating field, the ring is pushed away. The lower ring has been sawed through. There is an EMF generated, but no current flow, and hence no magnetic field is produced by the ring. Self-Inductance Back-EMF can be explained another way. As Faraday showed, EMF is induced whenever a wire cuts magnetic field lines. Consider the coil of wire shown in Figure 25-9. The current through the wire increases as we move from left to right. Current generates a magnetic field, shown by magnetic field lines. As the current and magnetic field increase, new lines are created. As the lines expand, they cut through the coil wires, generating an EMF to oppose the current changes. This induction of EMF in a wire carrying changing current is called self-inductance. The size of the EMF is proportional to the rate at which field lines cut through the wires. The faster you try to change the current, the larger the opposing EMF, and the slower the current change. If the current reaches a steady value, the magnetic field is constant, and the EMF is zero. When the current is decreased, an EMF is generated that tends to prevent the reduction in magnetic field and current. Because of self-inductance, work has to be done to increase the current flowing through the coil. Energy is stored in the magnetic field. This is similar to the way a charged capacitor stores energy in the electric field between its plates. 25.2 FIGURE 25-9. As the current in the coil increases from left to right, the EMF generated by the current also increases. . Go With The Flow F. Y. I. Many modern automobiles have an electronic ignition system that varies the magnetic field. An aluminum armature with 4, 6, or 8 protrusions (depending on the number of spark plugs) spins. Each protrusion in turn passes through the magnetic field, causing it to vary. Effects of Changing Magnetic Fields: Induced EMF 525 Transformers POCKET Inductance between coils is the basis for the operation of a transformer. A transformer is a device used to increase or decrease AC voltages. Transformers are widely used because they change voltages with essentially no loss of energy. Self-inductance produces an EMF when current changes in a single coil. A transformer has two coils, electrically insulated from each other, but wound around the same iron core. One coil is called the primary coil. The other coil is called the secondary coil. When the primary coil is connected to a source of AC voltage, the changing current creates a varying magnetic field. The varying magnetic field is carried through the core to the secondary coil. In the secondary coil, the varying field induces a varying EMF. This effect is called mutual inductance. The EMF induced in the secondary coil, called the secondary voltage, is proportional to the primary voltage. The secondary voltage also depends on the ratio of turns on the secondary to turns on the primary. LAB SLOW MOTOR Make a series circuit with a miniature DC motor, an ammeter, and a DC power supply. Hook up a voltmeter in parallel across the motor. Adjust the setting on the power supply so that the motor is running at medium speed. Make a data table to show the readings on the ammeter and voltmeter. Predict what will happen to the readings on the circuit when you hold the shaft and keep it from turning. Try it. Explain the results. secondary voltage number of turns on secondary primary voltage number of turns on primary I~;~ z;1 Ns Vs = -Vp Np A transformer uses two coupled coils to increase or decrease the voltage in an AC circuit. If the secondary voltage is larger than the primary voltage, the transformer is called a step-up transformer. If the voltage out of the transformer is smaller than the voltage put in, then it is called a step-down transformer. In an ideal transformer, the electric power delivered to the secondary circuit equals the power supplied to the primary. An ideal transformer dissipates no power itself. Since P = VI, Vp Ip = v, Is. The current that flows in the primary depends on how much current is required by the secondary circuit. Is Ip FIGURE 25-10. For a transformer, the ratio of input voltage to output voltage depends upon the ratio of the number of turns on the primary to the number of turns on the secondary. Primary 100V - lOA L ~3 -------r-rl 1000W. I ~ 5 turns 20 turns Core Electromagnetic Induction I Secondary 200V 400 V -- __ 1000V 2.5A . Vp _ Np v, Ns Primary -'I' --- Step-up transformer a 526 Secondary = lOA 2A 2000W 1000W 2000W b Step-down transformer A step-up transformer increases voltage; the current in the primary circuit is greater than that in the secondary. In a step-down transformer, the current is greater in the secondary circuit than it is in the primary. FIGURE25-11. If the input voltage is connected to the coils on the left, with the larger number of turns, the transformer functions as a stepdown transformer. If the input voltage is connected at the right, it is a step-up transformer. Example Problem Step-Up Transformer A certain step-up transformer has 2.00 x 102 turns on its primary coil and 3.00 x 103 turns on its secondary coil. a. The primary coil is supplied with an alternating current at an effective voltage of 90.0 V. What is the voltage in the secondary circuit? b. The current flowing in the secondary circuit is 2.00 A. What current flows in the primary circuit? c. What is the power in the primary circuit? in the secondary circuit? Given: Np = 2.00 Unknowns: a. v, b. Basicequations: x 102 3 Ns Vp = = 3.00 X 10 90.0 V Is = 2.00 A v, a.-=- v, b. Vp/p Ip c. P Ns Np = Vs/s Solution: V N = -'2 or V = VpNs Ns Np a. -E v, (90.0 V)(3.00 x 103) _ 3 2.00 X 102 - 1.35 x 10 V b V . c. I pp = V I or I ssp = Vs/s Vp = (1350 V)(2.00 A) 90.0 V - 30.0 A Pp = Vp Ip = (90.0 V)(30.0 A) r, = v, Is = (1350 V)(2.00 A) = 2.70 x 103 W 2.70 x 103 W Practice Problems In all problems, effective currents and voltages are indicated. 9. A step-down transformer has 7500 turns on its primary and 125 turns on its secondary. The voltage across the primary is 7200 V. a. What voltage is across the secondary? b. The current in the secondary is 36 A. What current flows in the primary? 10. The secondary of a step-down transformer has 500 turns. The primary has 15 000 turns. a. The EMF of the primary is 3600 V. What is the EMF of the secondary? b. The current in the primary is 3.0 A. What current flows in the secondary? 25.2 F.Y.I. The transformerswith the largest power rating in the world changes765 kV to 345 kV. Their power handlingcapacity is 1 500 OOOW. Effects of Changing Magnetic Fields: Induced EMF 527 FIGURE 25-12. Transformers are used to reduce voltages to consumer levels at the points of use. HISTORY CONNECTION In the late 1800s, there was much debate in the United States over the best way to transmit power from power plants to consumers. The existing plants transmitted direct current (DC), but DC had serious limitations. A key decision was made to use alternating current (AC) in the new hydroelectric power plant at Niagara Falls. With the first successful transmission of AC to Buffalo, New York in 1896, the Niagara Falls plant paved the way for the development of AC power plants across the country. It literally provided the spark for the rapid growth of United States cities and industries that followed. 528 Electromagnetic Induction 11. An ideal step-up transformer's primary circuit has 500 turns. Its secondary circuit has 15 000 turns. The primary is connected to an AC generator having an EMF of 120 V. a. Calculate the EMF of the secondary. b. Find the current in the primary if the current in the secondary is 3.0 A. c. What power is drawn by the primary? What power is supplied by the secondary? ~ 12. A step-up transformer has 300 turns on its primary and 90 000 4 (9.000 X 10 ) turns on its secondary. The EMF of the generator to which the primary is attached is 60.0 V. a. What is the EMF in the secondary? b. The current flowing in the secondary is 0.50 A. What current flows in the primary? As was discussed in Chapter 23, long-distance transmission of electric energy is economical only if low currents and very high voltages are used. Step-up transformers are used at power sources to develop voltages as high as 480 000 V. The high voltage reduces the current flow required in the transmission lines, keeping /2R losses low. When the energy reaches the consumer, step-down transformers provide appropriately low voltages for consumer use. There are many other important uses of transformers. Television picture tubes require up to 25 kV, developed by a transformer within the set. The spark or ignition coil in an automobile is a transformer designed to step up the 12 V from the battery to thousands of volts. The "points" interrupt the DC current from the battery to produce the changing magnetic field needed to induce EMF in the secondary coil. Some arc welders require currents of 104 A. Large step-down transformers are used to provide these currents, which can heat metals to 3000°C or more. CONCEPT REVIEW 2.1 You hang a coil of wire with its ends joined so it can swing easily. If you now plunge a magnet into the coil, the coil will swing. Which way will it swing with respect to the magnet and why? 2.2 If you unplug a running vacuum cleaner from the wall outlet, you are much more likely to see a spark than if you unplug a lighted lamp from the wall. Why? 2.3 Frequently, transformer windings that have only a few turns are made of very thick (low-resistance) wire, while those with many turns are made of thin wire. Why is this true? 2.4 Critical Thinking; Would permanent magnets make good transformer cores? Explain. P hysics and society WEAK ELECTROMAGNETIC FIELDS-A HEALTH CONCERN? A lternating currents, such as those in household wiring, produce electric and magnetic fields. The very low AC frequency is call Extremely Low Frequency, or ELF. The many sources of ELF electric and magnetic fields include power lines, home wiring, electric clocks, electric blankets, televisions and computer terminals. Twenty years ago, most scientists would have claimed that very weak electric and magnetic fields produced by ELFs could not affect living systems. Electric fields do exert forces on the ions in cellular fluids, and changing magnetic fields can induce such electric fields. Fields normally present in cells, however, are much larger than fields induced by ELFs, and, unlike ultraviolet radiation, ELFs can't break chemical bonds. Recently, however, experiments have shown that cells are sensitive to even very weak ELF fields. They can affect flow of ions across cell membranes, synthesis of DNA, and the response of cells to hormones. Abnormal development of chick embryos has been seen. The experimental results, however, are very complex. Some effects of ELFs occur only at certain frequencies or amplitudes. Others occur only if the fields are turned on or off abruptly. Finally, for most environmental health hazards the larger the exposure, or dose, the larger the effect. For ELFs, there is no clear way to define or measure dose. Some action has already been taken to reduce ELFfields. Electric blankets producing much lower magnetic fields are now sold. Several computer manufacturers sell terminals that produce smaller fields. Without knowing how to measure dose, however, it is not clear if such changes are enough to solve the problem. Is there an association between cancer and exposure to ELF? Some studies found small increases in leukemia, breast cancer, and brain cancer. Studies of users of electric blankets have shown no effects on men, but increases in cancers and brain tumors in children whose mothers slept under electric blankets while pregnant. Studies to find the causes will take years and may not have conclusive results. In the meantime, what should be done? DEVELOPING A VIEWPOINT Read articles about ELFs and come to class ready to discuss the following questions. 1. What do you think should be done? Should no action be taken until there is conclusive evidence of health hazards of ELFs?Or, is there enough reason for concern to take measures to limit exposure to ELFs? 2. Suppose a study finds many cancer cases among people who live near power lines. Would this prove that ELF fields from power lines cause cancer? 3. What steps could you take to reduce exposure to ELF? 4. What could utility companies do to reduce ELF fields? SUGGESTED READINGS Noland, David. "Power Play." 10 (12), 62-68, December, 1989. Pool, Robert. "Electromagnetic Fields: The Biological Evidence." Science 249, 13781381, September 21, 1990. Raloff, Janet. "EPA Suspects ELF Fields Can Cause Cancer." Science News 137, 404-405, June 30, 1990. Discover 25.2 Effects of Changing Magnetic Fields: Induced EMF 529 CHAPTER 25 REVIEW···························· ------------~~=---~~~~~~~~~ SUMMARY 25.1 Creating Electric Magnetic Fields KEY TERMS Current from Changing · Michael Faraday and Joseph Henry discovered that if a wire moves through a magnetic field, an electric current can be induced in the wire. · The direction that current flows in a wire moving through a magnetic field depends upon the direction of the motion of the wire and the direction of the magnetic field. · The current produced depends upon the angle between the velocity of the wire and the magnetic field. Maximum current occurs when the wire is moving at right angles to the field. · Electromotive force, EMF, is the increased potential of charges in the moving wire. EMF is measured in volts. · The EMF in a straight length of wire moving through a uniform magnetic field is the product of the magnetic induction, B, the length of the wire, L, and the component of the velocity of the moving wire, v, perpendicular to the field. · An electric generator consists of a number of wire loops placed in a magnetic field. Because each side of the coil moves alternately up and down through the field, the current alternates direction in the loops. The generator develops alternating voltage and current. · A generator and a motor are similar devices. A generator converts mechanical energy to electric energy; a motor converts electric energy to mechanical energy. 25.2 Effects of Changing Induced EMF MagnetiC Fields: · Lenz's law states: An induced current is always produced in a direction such that the magnetic field resulting from the induced current opposes the change in the field that is causing the induced current. · A transformer has two coils wound about the same core. An AC current through the primary coil induces an alternating EMF in the secondary coil. The voltages in alternating current circuits may be increased or decreased by transformers. 530 Electromagnetic Induction electromagnetic induction electromotive force electric generator Lenz's law self-inductance transformer primary coil secondary coil mutual inductance step-up transformer step-down transformer REVIEWING CONCEPTS 1. How are Oersted's and Faraday's results similar? How are they different? 2. Matt has a coil of wire and a bar magnet. Describe how Matt could use them to generate an electric current. 3. What does EMF stand for? Why is the name inaccurate? 4. What is the armature of an electric generator? 5. Why is iron used in an armature? 6. What is the difference between a generator and a motor? 7. List the major parts of an AC generator. 8. Why is the effective value of an AC current less than the maximum value? 9. Water trapped behind Hoover Dam turns turbines that rotate generators. List the forms of energy between the stored water and the final electricity produced. 10. State Lenz's law. 11. What produces the back-EMF of an electric motor? 12. Why is there no spark when you close a switch, putting current through an inductor, but there is a spark when you open the switch? 13. Why is the self-inductance of a coil a major factor when the coil is in an AC circuit but a minor factor when the coil is in a DC circuit? 14. Explain why the word "change" appears so often in this chapter. 15. Upon what does the ratio of the EMF in the primary of a transformer to the EMF in the secondary of the transformer depend? APPLYING CONCEPTS 1. What is the difference between the current generated in a wire when the wire is moved up through a horizontal magnetic field and the current generated when the wire is moved down through the same field? 2. Substitute units to show that the unit of BLv is volts. 3. If the strength of a magnetic field is fixed, in what three ways can you vary the size of the EMF you can generate? 4. When a wire is moved through a magnetic field, resistance of the closed circuit affects a. current only. c. both. b. EMF only. d. neither. 5. As Logan slows his bike, what happens to the EMF produced by his bike's generator? 6. A hand-cranked generator is dropped, weakening the permanent magnet. How does this affect the speed at which the generator must be cranked to keep the same EMF? 7. The direction of AC voltage changes 120 times each second. Does that mean a device connected to an AC voltage alternately delivers and accepts energy? 8. A wire segment is moved horizontally between the poles of a magnet as shown in Figure 25-13. What is the direction of the induced current? 12. 13. 14. 15. 16. present AC system. What are the reasons the Westinghouse system was adopted? A transformer is connected to a battery through a switch. The secondary circuit contains a light bulb. Which of these statements best describes when the lamp will be lighted? a. as long as the switch is closed b. only the moment the switch is closed c. only the moment the switch is opened Explain. An inventor claims that a very efficient transformer will step up power as well as voltage. Should we believe this? Explain. Suppose a magnetic field is directed vertically downward. You move a wire at constant speed, first horizontally, then downward at 45°, then directly down. a. Compare the induced EMF for the three motions. b. Explain the variations in voltage. The direction of Earth's magnetic field in the northern hemisphere is downward and to the north. If an east-west wire moves from north to south, in which direction does the current flow? Steve is moving a loop of copper wire down through a magnetic field B, as shown in Figure 25-16. a. Will the induced current move to the right or left in the wire segment in the diagram? b. As soon as the wire is moved in the field, a current appears in it. Thus, the wire segment is a current-carrying wire located in a magnetic field. A force must act on the wire. What will be the direction of the force acting on the wire due to the induced current? FIGURE 25-13. Use with Applying Concept S. 9. M.artha makes an electromagnet by winding wire around a large nail. If she connects the magnet to a battery, is the current larger just after she makes the connection or several tenths of seconds after the connection is made? Or is it always the same? Explain. 10. A wire segment is moving downward through the poles of a magnet as shown in Figure 2514. What is the direction of the induced current? 11. Thomas Edison proposed distributing electrical energy using constant voltages (DC). George Westinghouse proposed using the Down FIGURE 25-14. Use with Applying Concepts 10 and 16. 17. Steve, a physics instructor, drops a magnet through a copper pipe, Figure 25-15. The magnet falls very slowly and the class concludes that there must be some force opposing gravity. Chapter 25 Review 531 a. What is the direction of the current induced in the pipe by the falling magnet if the S-pole is toward the bottom? b. The induced current produces a magnetic field. What is the direction of the field? c. How does this field reduce the acceleration of the falling magnet? FIGURE 25-15. Use with Applying Concepts 17. 18. Why is a generator more difficult to rotate when it is connected to a circuit and supplying current than it is when it is standing alone? PROBLEMS 25.1 Creating Electric Magnetic Fields Current From Changing 1. A wire segment, 31 m long, moves straight up through a 4.0 x 1O-2-T magnetic field at a speed of 15.0 m/s. What EMF is induced in the wire? 2. A wire, 20.0 m long, moves at 4.0 m/s perpendicularly through a 0.50-T magnetic field. What EMF is induced in the wire? FIGURE 25-16. Use with Problem 2. 3. An airplane traveling at 950 km/h passes over a region where Earth's magnetic field is 4.5 x 10-5 T and is nearly vertical. What voltage is induced between the plane's wing tips, which are 75 m apart? 532 Electromagnetic Induction 4. A straight wire, 0.75 m long, moves upward through a horizontal 0.30- T magnetic field at a speed of 16 m/s. a. What EMF is induced in the wire? b. The wire is a part of a circuit with a total resistance of 11 D. What current flows in the circuit? ~ 5. A 40-cm wire is moved perpendicularly through a magnetic field of 0.32 T with a velocity of 1.3 m/s. If this wire is connected into a circuit of 10-D resistance, how much current is flowing? ~ 6. Jennifer connects both ends of a copper wire, total resistance 0.10 D, to the terminals of a galvanometer. The galvanometer has a resistance of 875 D. Jennifer then moves a 10.0-cm segment of the wire upward at 1.0 m/s through a 2.0 x 1O-2-T magnetic field. What current will the galvanometer indicate? ~ 7. The direction of a 0.045-T magnetic field is 60° above the horizontal. A wire, 2.5 m long, moves horizontally at 2.4 m/s. a. What is the vertical component of the magnetic field? b. What EMF is induced in the wire? 8. An EMF of 0.0020 V wire when it is moving a uniform magnetic 4.0 m/s. What is the field? is induced in a 10-cm perpendicularly across field at a speed of size of the magnetic 9. At what speed would a 0.2-m length of wire have to move across a 2.5- T magnetic field to induce an EMF of 10 V? 10. An AC generator develops a maximum EMF of 565 V. What effective EMF does the generator deliver to an external circuit? 11. An AC generator develops a maximum voltage of 150 V. It delivers a maximum current of 30.0 A to an external circuit. a. What is the effective voltage of the generator? b. What effective current does it deliver to the external circuit? c. What is the effective power dissipated in the circuit? 12. An electric stove is connected to an AC source with effective voltage of 240 V. a. Find the maximum voltage across one of the stove's elements when it is operating? b. The resistance of the operating element is 11 n. What effective current flows through it? ~ 13. A generator at Hoover Dam can supply 375 MW (375 x 106 W) of electrical power. Assume that the turbine and generator are 85% efficient. a. Find the rate which falling water must supply energy to the turbine. b. The energy of the water comes from a change in potential energy, mgh. What is the needed change in potential energy each second? c. If the water falls 22 m, what is the mass of the water that must pass through the turbine each second to supply this power? 25.2 Effects of Changing Magnetic Fields: Induced EMF 14. The primary of a transformer has 150 turns. It is connected to a 120-V source. Calculate the number of turns on the secondary needed to supply these voltages. a. 625 V b. 35 V c. 6.0 V 15. A step-up transformer has 80 turns on its primary. It has 1200 turns on its secondary. The primary is supplied with an alternating current at 120 V. a. What voltage is across the secondary? b. The current in the secondary is 2.0 A. What current flows in the primary circuit? c. What is the power input and output of the transformer? 16. A portable computer requires an effective voltage of 9.0 volts from the 120 -V line. a. If the primary of the transformer has 475 turns, how many does the secondary have? b. A 125-mA current flows through the computer. What current flows through the transformer's primary? 17. In a hydroelectric plant, electricity is generated at 1200 V. It is transmitted at 240 000 V. a. What is the ratio of the turns on the primary to the turns on the secondary of a transformer connected to one of the generators? b. One of the plant generators can deliver 40.0 A to the primary of its transformer. What current is flowing in the secondary? 18. A hair dryer uses 10 A at 120 V. It is used with a transformer in England, where the line voltage is 240 V. a. What should be the ratio of the turns of the transformer? b. What current will it draw from the 240-V line? 19. A step-up transformer is connected to a generator that is delivering 125 V and 95 A. The ratio of the turns on the secondary to the turns on the primary is 1000 to 1. a. What voltage is across the secondary? b. What current flows in the secondary? ~ 20. A 150-W transformer has an input voltage of 9.0 V and an output current of 5.0 A. a. Is this a step-up or step-down transformer? b. What is the ratio of output voltage to input voltage? ~ 21. A transformer has input voltage and current of 12 V and 3.0 A respectively, and an output current of 0.75 A. If there are 1200 turns on the secondary side of the transformer, how many turns are on the primary side? ~ 22. Scott connects a transformer to a 24-V source and measures 8.0 V at the secondary. If the primary and secondary were reversed, what would the new output voltage be? USING LAB SKILLS 1. After doinq the Pocket Lab on page 518, predict what will happen if the magnet is kept stationary and the coil moves. Try it. What happens if the coil and magnet move together? Try it. THINKING PHYSIC-LY 1. A bike's headlamp is powered by a generator that rubs against a wheel. Why is it harder to pedal when the generator is lighting the lamp? 2. Suppose an "anti-Lenz's law" existed that meant a force was exerted to increase the change in magnetic field. Thus, when more electrical energy was demanded from a generator, the force needed to turn it would be reduced. What conservation law would be violated by this new "law"? Explain. Chapter 25 Review 533