Physics
Induced Currents
Induced currents refer to the production of an electric current in a conductor due to a changing magnetic field. This phenomenon is described by Faraday's law of electromagnetic induction, which states that a changing magnetic field induces an electromotive force (EMF) in a conductor, resulting in the generation of an induced current. Induced currents are fundamental to understanding the relationship between electricity and magnetism.
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11 Key excerpts on "Induced Currents"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
550 Chapter 22 | Electromagnetic Induction 22.1 | Induced Emf and Induced Current There are a number of ways a magnetic field can be used to generate an electric current, and Figure 22.1 illustrates one of them. This drawing shows a bar magnet and a helical coil of wire to which an ammeter is connected. When there is no relative motion between the magnet and the coil, as in part a of the drawing, the ammeter reads zero, indicating that no current exists. However, when the magnet moves toward the coil, as in part b, a current I appears. As the magnet approaches, the magnetic field B B that it creates at the location of the coil becomes stronger and stronger, and it is this changing field that produces the current. When the magnet moves away from the coil, as in part c, a current is also pro- duced, but with a reversed direction. Now the magnetic field at the coil becomes weaker as the magnet moves away. Once again it is the changing field that generates the current. A current would also be created in Figure 22.1 if the magnet were held stationary and the coil were moved, because the magnetic field at the coil would be changing as the coil approached or receded from the magnet. Only relative motion between the magnet and the coil is needed to generate a current; it does not matter which one moves. The current in the coil is called an induced current because it is brought about (or “in- duced”) by a changing magnetic field. Since a source of emf (electromotive force) is always needed to produce a current, the coil itself behaves as if it were a source of emf. This emf is known as an induced emf. Thus, a changing magnetic field induces an emf in the coil, and the emf leads to an induced current. 22 | Electromagnetic Induction © Jeff Greenberg/Age Fotostock Electric guitars are famous for their amplified and manipulatable sound. To produce this sound, virtually all of them have one or more electro- magnetic pickups located beneath the strings (see Section 22.6).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
22.1 | Induced Emf and Induced Current There are a number of ways a magnetic field can be used to generate an electric current, and Figure 22.1 illustrates one of them. This drawing shows a bar magnet and a helical coil of wire to which an ammeter is connected. When there is no relative motion between the magnet and the coil, as in part a of the drawing, the ammeter reads zero, indicating that no current exists. However, when the magnet moves toward the coil, as in part b, a current I appears. As the magnet approaches, the magnetic field B B that it creates at the location of the coil becomes stronger and stronger, and it is this changing field that produces the current. When the magnet moves away from the coil, as in part c, a current is also pro- duced, but with a reversed direction. Now the magnetic field at the coil becomes weaker as the magnet moves away. Once again it is the changing field that generates the current. A current would also be created in Figure 22.1 if the magnet were held stationary and the coil were moved, because the magnetic field at the coil would be changing as the coil approached or receded from the magnet. Only relative motion between the magnet and the coil is needed to generate a current; it does not matter which one moves. The current in the coil is called an induced current because it is brought about (or “in- duced”) by a changing magnetic field. Since a source of emf (electromotive force) is always needed to produce a current, the coil itself behaves as if it were a source of emf. This emf is known as an induced emf. Thus, a changing magnetic field induces an emf in the coil, and the emf leads to an induced current. Electric guitars are famous for their amplified and manipulatable sound. To produce this sound, virtually all of them have one or more electro- magnetic pickups located beneath the strings (see Section 22.6).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
LEARNING OBJECTIVES After reading this module, you should be able to... 22.1 Predict when an induced current will flow. 22.2 Solve motional emf problems. 22.3 Calculate magnetic flux. 22.4 Solve problems using Faraday’s law of induction. 22.5 Predict the direction of an induced current using Lenz’s law. 22.6 Describe how sound is reproduced via induction. 22.7 Solve problems involving generators. 22.8 Define mutual induction and self- inductance. 22.9 Solve problems involving transformers. © Jeff Greenberg/Age Fotostock CHAPTER 22 Electromagnetic Induction Electric guitars are famous for their amplified and manipulatable sound. To produce this sound, virtually all of them have one or more electromagnetic pickups located beneath the strings (see Section 22.6). These pickups work because of electromagnetic induction, which is the process by which a magnet is used to create or induce an emf in a coil of wire. In this photograph the pickup is indicated by the shiny rectangle in the white area. 22.1 Induced Emf and Induced Current There are a number of ways a magnetic field can be used to generate an electric cur- rent, and Interactive Figure 22.1 illustrates one of them. This drawing shows a bar magnet and a helical coil of wire to which an ammeter is connected. When there is no relative motion between the magnet and the coil, as in part a of the drawing, the ammeter reads zero, indicating that no current exists. However, when the magnet moves toward the coil, as in part b, a current I appears. As the magnet approaches, the magnetic field B → that it creates at the location of the coil becomes stronger and stron- ger, and it is this changing field that produces the current. When the magnet moves away from the coil, as in part c, a current is also produced, but with a reversed direc- tion. Now the magnetic field at the coil becomes weaker as the magnet moves away. Once again it is the changing field that generates the current.
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2023(Publication Date)
- Società Editrice Esculapio(Publisher)
The appearance of a current is not, however, the main effect: if the circuit is opened in a whatever point, a voltage, independent of the opening position, is measured between the circuit extremities. The just described phenomenon is called electromagnetic induction. Its main effect is the appearance of an induced electromotive force E i in a circuit and, as a secondary effect, of an induced current, caused by the electromotive force that makes the free electrons move in the coil, if the circuit is closed. The magnitude of the induced electromotive force only depends on the time rate of change of the magnetic flux linked to the circuit. Experiments show that Faraday’s law (1791-1867) E i = − dΦ B dt , which states that whenever the flux of a magnetic field linked to a closed, or open in a point, circuit changes in time, an electromotive force E i , moment by moment equal to the sign in- verted derivative of the magnetic flux with respect to time, i.e. the opposite of the time rate of change of the magnetic flux, is generated, governs electromagnetic induction. 12.3 Lenz’s law The minus sign in Faraday’s law expresses Lenz’s law (1804-1865) which states that the direction of the electromotive force E i is such that it induces a current i which gen- erates, in its turn, an induced magnetic field B i whose flux linked to the circuit tends to compensate the flux change which generated it. In other words, the effect is such that it opposes the cause which produced it. Consider, for instance, the case of a moving magnet. The B field generated by the mag- net is not uniform, so, if the magnet moves towards the coil, its magnetic flux linked to it increases, while, if it moves away from the coil, the linked flux decreases.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- University Publications(Publisher)
This case is called an induced EMF. On the other hand, when the magnet is stationary and the conductor is rotated, the moving charges experience a magnetic force (as described by the Lorentz force law), and this magnetic force pushes the charges through the wire. This case is called motional EMF. Electrical motor An electrical generator can be run backwards to become a motor. For example, with the Faraday disc, suppose a DC current is driven through the conducting radial arm by a voltage. Then by the Lorentz force law, this traveling charge experiences a force in the magnetic field B that will turn the disc in a direction given by Fleming's left hand rule. In the absence of irreversible effects, like friction or Joule heating, the disc turns at the rate necessary to make d Φ B / dt equal to the voltage driving the current. ____________________ WORLD TECHNOLOGIES ____________________ Electrical transformer The EMF predicted by Faraday's law is also responsible for electrical transformers. When the electric current in a loop of wire changes, the changing current creates a changing magnetic field. A second wire in reach of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, a d Φ B / d t . Therefore, an electromotive force is set up in the second loop called the induced EMF or transformer EMF . If the two ends of this loop are connected through an electrical load, current will flow. Magnetic flow meter Faraday's law is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called magnetic flow meters. The induced voltage ℇ gen-erated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by: , where ℓ is the distance between electrodes in the magnetic flow meter.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
This case is called an induced EMF. On the other hand, when the magnet is stationary and the conductor is rotated, the moving charges experience a magnetic force (as described by the Lorentz force law), and this magnetic force pushes the charges through the wire. This case is called motional EMF. Electrical motor An electrical generator can be run backwards to become a motor. For example, with the Faraday disc, suppose a DC current is driven through the conducting radial arm by a voltage. Then by the Lorentz force law, this traveling charge experiences a force in the magnetic field B that will turn the disc in a direction given by Fleming's left hand rule. In the absence of irreversible effects, like friction or Joule heating, the disc turns at the rate necessary to make d Φ B / dt equal to the voltage driving the current. Electrical transformer The EMF predicted by Faraday's law is also responsible for electrical transformers. When the electric current in a loop of wire changes, the changing current creates a changing ________________________ WORLD TECHNOLOGIES ________________________ magnetic field. A second wire in reach of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, a d Φ B / d t . Therefore, an electromotive force is set up in the second loop called the induced EMF or transformer EMF . If the two ends of this loop are connected through an electrical load, current will flow. Magnetic flow meter Faraday's law is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called magnetic flow meters. The induced voltage ℇ generated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by: , where ℓ is the distance between electrodes in the magnetic flow meter.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
This drawing shows a bar magnet and a helical coil of wire to which an ammeter is connected. When there is no relative motion between the magnet and the coil, as in part a of the drawing, the ammeter reads zero, indicating that no current exists. However, when the magnet moves toward the coil, as in part b, a current I appears. As the magnet approaches, the magnetic field → B that it creates at the location of the coil becomes stronger and stronger, and it is this changing field that produces the current. When the magnet moves away from the coil, as in part c, a 694 CHAPTER 22 Electromagnetic Induction current is also produced, but with a reversed direction. Now the magnetic field at the coil becomes weaker as the magnet moves away. Once again it is the changing field that generates the current. A current would also be created in Interactive Figure 22.1 if the magnet were held stationary and the coil were moved, because the magnetic field at the coil would be changing as the coil approached or receded from the magnet. Only relative motion between the magnet and the coil is needed to generate a current; it does not matter which one moves. The current in the coil is called an induced current because it is brought about (or “induced”) by a changing magnetic field. Since a source of emf (electromotive force) is always needed to produce a current, the coil itself behaves as if it were a source of emf. This emf is known as an induced emf. Thus, a changing magnetic field induces an emf in the coil, and the emf leads to an induced current. THE PHYSICS OF . . . an automobile cruise control. Induced emf and induced current are frequently used in the cruise controls found in many cars. Interactive Figure 22.2 illustrates how a cruise control operates. Usually two magnets are mounted on opposite sides of the vehicle’s drive shaft, with a stationary sensing coil positioned nearby.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
This case is called an induced EMF. On the other hand, when the magnet is stationary and the conductor is rotated, the moving charges experience a magnetic force (as described by the Lorentz force law), and this magnetic force pushes the charges through the wire. This case is called motional EMF. Electrical motor An electrical generator can be run backwards to become a motor. For example, with the Faraday disc, suppose a DC current is driven through the conducting radial arm by a voltage. Then by the Lorentz force law, this traveling charge experiences a force in the magnetic field B that will turn the disc in a direction given by Fleming's left hand rule. In the absence of irreversible effects, like friction or Joule heating, the disc turns at the rate necessary to make d Φ B / dt equal to the voltage driving the current. ________________________ WORLD TECHNOLOGIES ________________________ Electrical transformer The EMF predicted by Faraday's law is also responsible for electrical transformers. When the electric current in a loop of wire changes, the changing current creates a changing magnetic field. A second wire in reach of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, a d Φ B / d t . Therefore, an electromotive force is set up in the second loop called the induced EMF or transformer EMF . If the two ends of this loop are connected through an electrical load, current will flow. Magnetic flow meter The third most common flowmeter behind differential pressure and positive displacement flow meters, is the magnetic flow meter , also technically an electromagnetic flow meter or more commonly just called a mag meter . A magnetic field is applied to the metering tube, which results in a potential difference proportional to the flow velocity per-pendicular to the flux lines. The physical principle at work is electromagnetic induction.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
• The units for magnetic flux are webers, where 1 Wb = 1 T · m 2 . • The induced emf in a closed loop due to a change in magnetic flux through the loop is known as Faraday’s law. If there is no change in magnetic flux, no induced emf is created. 13.2 Lenz's Law • We can use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs. • The direction of an induced emf always opposes the change in magnetic flux that causes the emf, a result known as Lenz’s law. Chapter 13 | Electromagnetic Induction 615 13.3 Motional Emf • The relationship between an induced emf ε in a wire moving at a constant speed v through a magnetic field B is given by ε = Blv. • An induced emf from Faraday’s law is created from a motional emf that opposes the change in flux. 13.4 Induced Electric Fields • A changing magnetic flux induces an electric field. • Both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday’s law. 13.5 Eddy Currents • Current loops induced in moving conductors are called eddy currents. They can create significant drag, called magnetic damping. • Manipulation of eddy currents has resulted in applications such as metal detectors, braking in trains or roller coasters, and induction cooktops. 13.6 Electric Generators and Back Emf • An electric generator rotates a coil in a magnetic field, inducing an emf given as a function of time by ε = NBAω sin(ωt) where A is the area of an N-turn coil rotated at a constant angular velocity ω in a uniform magnetic field B → . • The peak emf of a generator is ε 0 = NBAω . • Any rotating coil produces an induced emf. In motors, this is called back emf because it opposes the emf input to the motor. 13.7 Applications of Electromagnetic Induction • Hard drives utilize magnetic induction to read/write information. • Other applications of magnetic induction can be found in graphics tablets, electric and hybrid vehicles, and in transcranial magnetic stimulation.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near a bar magnet with a sliding electrical lead (Faraday's disk). Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically. An exception was Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's papers, the time varying aspect of electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is slightly different in form from the original version of Faraday's law, and doesn't cater for motionally induced EMF. Heaviside's version is the form recognized today in the group of equations known as Maxwell's equations. ____________________ WORLD TECHNOLOGIES ____________________ Lenz's law, formulated by Heinrich Lenz in 1834, describes flux through the circuit, and gives the direction of the induced electromotive force and current resulting from electromagnetic induction (elaborated upon in the examples below). Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G). Faraday's law as two different phenomena Some physicists have remarked that Faraday's law is a single equation describing two different phenomena: The motional EMF generated by a magnetic force on a moving wire, and the transformer EMF generated by an electric force due to a changing magnetic field.
eBook - PDFHalf-Hours with Great Scientists
The Story of Physics
- Charles G. Fraser(Author)
- 2019(Publication Date)
- University of Toronto Press(Publisher)
CHAPTER TWENTY-TWO Induced Currents T HE germs of the first four epochs in electricity, typified by the ideas of charge, conduction, influence, and current, we have found in the words and work of Thaïes, Gray, Canton, and Volta. In the present chapter occur the pregnant words which brought the fifth epoch of electricity into the world and the Electrical Age with all its blessings and abuses. This advancement was achieved largely by the application of Michael Faraday's discoveries in the world's affairs. Most of the currents used in the present age for household, industrial, and municipal purposes are Induced Currents, obtained from generators. FARADAY'S DISCOVERIES Although the voltaic battery yields continuous flow of electricity, yet it could not bring the electrical age because there was not enough zinc in the world to light all the streets and buildings and to run the factories. What was needed was some supply of electricity of much greater magnitude. The chief source of energy available, of sufficient magnitude, is mechanical energy (kinetic and potential), for example, the energy of waterfalls, winds, steam engines, and so forth. Faraday conjectured that a magnet should have in some way an electrical effect. He was searching for a new relation between magnetism and electricity. In Oersted's experiment the energy of electricity is converted into the kinetic energy of the needle, which is a magnet. Faraday knew that many energy transformations can be reversed. Thus in a steam engine, heat is transmuted into kinetic energy and contrariwise, when a boy slides down a bannister, kinetic energy is transformed into heat. Faraday asked himself how he could reverse the conditions of Oersted's experiment so as to obtain electrical energy from the kinetic energy of a magnet. By his experiments, he asked Nature this question. It took him seven years of patient and discouraging work 459 460 The Story of Electricity and Magnetism to find the answer.
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