Physics
Motional EMF
Motional EMF refers to the electromotive force induced in a conductor moving through a magnetic field. This phenomenon occurs when the conductor experiences a change in magnetic flux, resulting in the generation of an electric potential difference. Motional EMF is a key concept in understanding electromagnetic induction and is described by Faraday's law of electromagnetic induction.
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11 Key excerpts on "Motional EMF"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Would there be an induced current in the coil? 22.2 Motional EMF The Emf Induced in a Moving Conductor When a conducting rod moves through a constant magnetic field, an emf is induced in the rod. This special case of electromagnetic induction arises as a result of the magnetic force that acts on a moving charge (see Section 21.2). Consider the metal rod of length L moving to the right in Animated Figure 22.4a. The velocity → v of the rod is constant and is per- pendicular to a uniform magnetic field → B . Each charge q within the rod also moves with a velocity → v and experiences a magnetic force of magnitude F = ∣q∣υB, according to Equation 21.1. By using RHR-1, it can be seen that the mobile, free electrons are driven to the bottom of the rod, leaving behind an equal amount of positive charge at the top. (Remember to reverse the direction of the force that RHR-1 predicts, since the electrons have a negative charge. See Section 21.2.) The positive and negative charges accumulate until the attractive electric force that they exert on each other becomes equal in magnitude to the magnetic force. When the two forces balance, equilibrium is reached and no further charge separation occurs. The separated charges on the ends of the moving conductor give rise to an induced emf, called a Motional EMF because it originates from the motion of charges through a magnetic field. The emf exists as long as the rod moves. If the rod is brought to a halt, the magnetic force vanishes, with the result that the attractive electric force reunites the positive and negative charges and the emf disappears. The emf of the moving rod is analogous to the emf between the terminals of a battery. However, the emf of a battery is produced by chemical reactions, whereas the Motional EMF is created by the agent that moves the rod through the magnetic field (like the hand in Animated Figure 22.4b).
eBook - PDF- Bhag Singh Guru, Hüseyin R. Hiziroglu(Authors)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
The effects of the magnetic force on a charged particle are already known to us, so let us begin with this latter approach. 7.2 Motional electromotive force ................................. Let us consider a conductor moving with a uniform velocity u in the x direction, as depicted in Figure 7.1. In the region there also exists a 276 277 7.2 Motional electromotive force Figure 7.1 A conductor moving in a uniform magnetic field uniform flux density B such that B = − B a z . The magnetic force acting on each of the free electrons in the conductor is F = q e u × B = q e uB a y (7.1) where q e is the magnitude of the charge on an electron. Under the influence of this force the free electrons within the conductor will move from right to left. Such a migration of electrons will result in a net negative charge at the left end of the conductor and a net positive charge at the right end. Barnett was able to demonstrate that such a separation of charges does take place in a conductor moving in a magnetic field. He managed to cut the conductor in the middle while it was still in motion. When the two pieces of the conductor were brought to rest, one was found to be positively charged while the other was negatively charged. The force per unit charge is the electric field intensity E , thus we obtain an expression for the E field from (7.1) as E = u × B = uB a y (7.2) Since the electric field as given by (7.2) is established by a magnetic field, it is referred to as the induced electric field . As the E field is a result of the motion of a conductor in the magnetic field, it is also called the motional electric field . Note that the induced electric field is perpendicular to the plane containing u and B . We will later show that the induced electric field is a nonconservative field . The induced electric field is tangential to the surface of the conductor.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
22.2 Motional EMF 627 In each of the previous examples, both an emf and a current are induced in the coil because the coil is part of a complete, or closed, circuit. If the circuit were open—perhaps because of an open switch—there would be no induced current. However, an emf would still be induced in the coil, whether the current exists or not. Changing a magnetic field and changing the area of a coil are methods that can be used to create an induced emf. The phenomenon of producing an induced emf with the aid of a magnetic field is called electromagnetic induction. The next section discusses yet another method by which an induced emf can be created. Check Your Understanding (The answer is given at the end of the book.) 1. Suppose that the coil and the magnet in Interactive Figure 22.1a were each moving with the same velocity relative to the earth. Would there be an induced current in the coil? 22.2 Motional EMF The Emf Induced in a Moving Conductor When a conducting rod moves through a constant magnetic field, an emf is induced in the rod. This special case of electromagnetic induction arises as a result of the magnetic force that acts on a moving charge (see Section 21.2). Consider the metal rod of length L moving to the right in Animated Figure 22.4a. The velocity v → of the rod is constant and is perpendicular to a uniform magnetic field B → . Each charge q within the rod also moves with a velocity v → and experiences a magnetic force of magnitude F = ∣ q∣ B, according to Equation 21.1. By using RHR-1, it can be seen that the mobile, free electrons are driven to the bottom of the rod, leaving behind an equal amount of positive charge at the top. (Remember to reverse the direction of the force that RHR-1 predicts, since the electrons have a negative charge. See Section 21.2.) The positive and negative charges accumulate until the attractive electric force that they exert on each other becomes equal in magnitude to the magnetic force.
eBook - PDFElectromagnetism for Engineers
An Introductory Course
- P. Hammond(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
describes a conservative field and is associated with magnetic potentials and H2 describes a non-conservative field and is associated with magnetomotive force. We now have a parallel situation in electricity. The electrostatic field strength E^ is due to electric charges and is associated with a conservative field and potential, while Electromagnetic Induction 109 ^ = E. electrostatic (6.17) In Section 4.4 we pointed out that an electromotive force is necessary to circulate electric current and that most generators rely for their electromotive force on the motion of conductors through magnetic fields. Let us consider this process in detail. Figure 6.7 shows a conductor of length / moving with £2 ''vB F IG. 6.7 Motional electric field strength in a conductor velocity υ across a uniform magnetic field B. The charges in the conductor will experience an electric field strength ν Β and the free electrons will move as far as they can, i.e. a surface charge will appear on the conductor (Fig. 6.8). When the electrons cease to move, the amount of the surface charge will be such as to provide an electrostatic field strength which is equal and opposite to vB. The F IG. 6.8 Electrostatic field cancels motional field the motional electric field strength of eqn. (6.16) is associated with a non-conservative field and electromotive force. Just as the total magnetic field strength is the sum of and so is the total electric field strength experienced by a charge the sum of the two components and £2· 110 Electromagnetism for Engineers V = -E , d/ ^E^ál = vBl (6.18) The electromotive force will be e.m.f. = E2 dl = vBl (6.19) Thus the e.m.f. and the p.d. are equal. So far the moving conductor does not supply current, because there is no circuit, but now consider the arrangement of Fig. 6.9 where there is a closed circuit. A thick conductor slides with velocity ν between two thick conducting bars through a magnetic field B.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Conduction electrons will accumulate, therefore, at the bottom of the rod, leaving a net positive charge at the top of the rod. This separation of charge creates an electric field directed down the rod. The charge separation contin- ues until the electric force on the charges is equal to the magnetic force. The magnitude of the magnetic force on a change is given by F q vB = (Equation 21.2.1), while the electric force is given by F q E = (Equation 18.3.1). Equating the electric and magnetic forces, we have q E q vB = and E vB = Induced Emf and Motional EMF | 607 Example 22.1.1 illustrates a simple way to generate electricity using Motional EMF. From V E s ∆ = ∆ (Equation 19.1.2), which relates changes in electric potential to the electric field, we have V EL ∆ = , which is the magnitude of the potential difference between the ends of the rod. This is the Motional EMF E , so substituting E L E / = into E vB = gives L vB E/ = . Multiplying both sides by L, we arrive at Equation 22.1.1: vBL = E Example 22.1.1 Generating Electricity Using Motional EMF The diagram illustrates a method by which useful electrical energy may be generated by Motional EMF. A conducting rod slides to the right along parallel conducting rails that are connected to a resistor (in this case, a light bulb) whose resistance is 15.5 Ω. The distance between the rails is L 1.40 m = and the rod moves at a constant speed of / 2.34 m s. The rod and rails form a circuit and there is a magnetic field of magnitude 0.560 T directed into the screen, as shown. B I I v L What are (a) the emf produced by the motion of the rod, (b) the current in the circuit, and (c) the power dissipated by the resistor? Identify The moving rod acts like a battery, supplying the emf that generates the current. We will assume that the resistance of the rod and the rails is negligible. The Motional EMF is directed up the moving rod, which is determined by applying the magnetic force right-hand rule to the rod.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
By using RHR‐1, it can be seen that the mobile, free electrons are driven to the bottom of the rod, leaving behind an equal amount of positive charge at the top. (Remember to reverse the direction CHAPTER 22 Electromagnetic induction 613 of the force that RHR‐1 predicts, since the electrons have a negative charge. See section 21.2.) The positive and negative charges accumulate until the attractive electric force that they exert on each other becomes equal in magnitude to the magnetic force. When the two forces balance, equilibrium is reached and no further charge separation occurs. The separated charges on the ends of the moving conductor give rise to an induced emf, called a Motional EMF because it originates from the motion of charges through a magnetic field. The emf exists as long as the rod moves. If the rod is brought to a halt, the magnetic force vanishes, with the result that the attractive electric force reunites the positive and negative charges and the emf disappears. The emf of the moving rod is analogous to the emf between the terminals of a battery. However, the emf of a battery is produced by chemical reactions, whereas the Motional EMF is created by the agent that moves the rod through the magnetic field (like the hand in figure 22.4b.) FIGURE 22.4 (a) When a conducting rod moves at right angles to a constant magnetic field, the magnetic force causes opposite charges to appear at the ends of the rod, giving rise to an induced emf. (b) The induced emf causes an induced current I to appear in the circuit. Conducting rod + + + – (a) B L – – v Conducting rail + – (b) I I I L v The fact that the electric and magnetic forces balance at equilibrium in figure 22.4a can be used to determine the magnitude of the Motional EMF ℰ . Acccording to equation 18.2, the magnitude of the electric force acting on the positive charge q at the top of the rod is Eq, where E is the magnitude of the electric field due to the separated charges.
eBook - ePub- S. Bobby Rauf(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
The term “electromotive” force stems from the early recognition of electrical current as something that consisted, strictly, of the movement of “electrons.” Nowadays, however, with the more recent breakthroughs in the renewable and non-traditional electrical power generating methods and systems like microbial fuel cells and hydrocarbon fuel cells, electrical power is being harnessed, more and more, in the form of charged particles that may not be electrons. In batteries, such as those used in automobiles, as we will see in the batteries chapter, the flow of current driven by voltage potential difference consists not only of negatively charged electrons, e −, but also types of ions, including H + and HSO 4 − ions. 1 Two, relatively putative, analogies for voltage in the mechanical and civil engineering disciplines are pressure and elevation. In the mechanical realm – or more specifically in the fluid and hydraulic systems – high pressure or pressure differential pushes fluid from one point to another and performs mechanical work. Similarly, voltage – in the form of voltage difference between two points, as with the positive and negative terminals of an automobile battery – moves electrons or charged particles through loads such as motors, coils, resistive elements, wires, or conductors. As electrons or charged particles are pushed through loads like motors, coils, resistive elements, light filaments, etc., electrical energy is converted into mechanical energy, heat energy, or light energy. In equipment like rechargeable batteries, during the charging process, applied voltage can push ions from one electrode (or terminal) to another and thereby “charge” the battery
eBook - PDFElectrotechnics N4 Student's Book
TVET FIRST
- SA Chuturgoon(Author)
- 2021(Publication Date)
- Troupant(Publisher)
So, let us highlight the differences between the two in order to avoid confusion. Electromotive force (emf) is the voltage (electrical potential) measured across the terminals of an electrical energy source of an open circuit, that is, when no current is flowing through the circuit. Important SI unit: a unit of measurement defined by the International System of Units (a metric system used in science and industry) dissipate: cause energy to be lost through its conversion to heat Electromotive ‘force’ is a misnomer . It is not a force measured in newtons but an electrical potential instead. Interesting open circuit: an incomplete electrical connection through which current cannot flow misnomer: a word or concept suggesting a meaning that is known to be wrong generator: a machine that converts one form of energy into another, especially mechanical energy into electrical energy solar energy: radiant energy emitted by the sun radiant: sending out light; shining or glowing brightly friction: the resistance that one surface encounters when moving over another 4 Module 1 TVET FIRST • The switch is open. • Current does not flow, so the light bulb does not glow. • The emf is measured across the energy source (the battery in this case). • The switch is closed. • Current is now flowing, so the light bulb glows. • The potential difference is measured across the energy source (the battery in this case). switch (open) light bulb (not glowing) battery emf + – Figure 1.2: Emf in an electric circuit Potential difference (PD) is the voltage (electrical potential) measured across the terminals of an electrical energy source of a closed circuit, that is, when current is flowing through the circuit. switch (closed) light bulb (glowing) battery PD + – I Figure 1.3: Potential difference in an electric circuit Figure 1.4 shows what actually happens in any electric circuit.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
Generators exploit Motional EMFs, which arise when you move a wire through a magnetic field. Figure 7.10 suggests a primitive model for a generator. In the shaded region there is a uniform magnetic field B, pointing into the page, and the resistor R represents whatever it is (maybe a light bulb or a toaster) we’re trying to drive current through. If the entire loop is pulled to the right with speed v, the charges in segment ab experience a magnetic force whose vertical component q v B drives current around the loop, in the clockwise direction. The emf is E = f mag · d l = v Bh , (7.11) where h is the width of the loop. (The horizontal segments bc and ad contribute nothing, since the force there is perpendicular to the wire.) Notice that the integral you perform to calculate E (Eq. 7.9 or 7.11) is carried out at one instant of time—take a “snapshot” of the loop, if you like, and work R v h c d x b a FIGURE 7.10 306 Chapter 7 Electrodynamics from that. Thus d l, for the segment ab in Fig. 7.10, points straight up, even though the loop is moving to the right. You can’t quarrel with this—it’s simply the way emf is defined—but it is important to be clear about it. In particular, although the magnetic force is responsible for establishing the emf, it is not doing any work—magnetic forces never do work. Who, then, is supplying the energy that heats the resistor? Answer: The person who’s pulling on the loop. With the current flowing, the free charges in segment ab have a vertical velocity (call it u) in addition to the horizontal velocity v they inherit from the motion of the loop. Accordingly, the magnetic force has a component quB to the left. To counteract this, the person pulling on the wire must exert a force per unit charge f pull = uB to the right (Fig. 7.11). This force is transmitted to the charge by the structure of the wire. Meanwhile, the particle is actually moving in the direction of the resultant ve- locity w, and the distance it goes is (h / cos θ ).
eBook - ePub- Jo Verhaevert, Christopher R. Robertson(Authors)
- 2024(Publication Date)
- Routledge(Publisher)
Chapter 5 Electromagnetism
DOI: 10.1201/9781003308294-5Learning Outcomes This chapter concerns the principles and laws governing electromagnetic induction and the concepts of self and mutual inductance. On completion of this chapter you should be able to use these principles to:- Understand the basic operating principles of motors and generators.
- Carry out simple calculations involving the generation of voltage, and the production of force and torque.
- Appreciate the significance of eddy current loss.
- Determine the value of inductors, and apply the concepts of self and mutual inductance to the operating principles of transformers.
- Calculate the energy stored in a magnetic field.
- Explain the principle of the moving coil metre and carry out simple calculations for the instrument.
5.1 Faraday’s Law of Electromagnetic Induction
It is mainly due to the pioneering work of Michael Faraday, in the nineteenth century, that the modern technological world exists as we know it. Without the development of the generation of electrical power, such advances would have been impossible. Thus, although the concepts involved with electromagnetic induction are very simple, they have far-reaching influence. Faraday’s law is best considered in two interrelated parts:- The value of emf induced in a circuit or conductor is directly proportional to the rate of change of magnetic flux linking with it.
- The polarity of such an emf, induced by an increasing flux, is opposite to that induced by a decreasing flux.
The key to electromagnetic induction is contained in part 1 of the law quoted above. Here, the words ‘rate of change’ are used. If there is no change in flux, or the way in which this flux links with a conductor, then no emf will be induced. The proof of the law can be very simply demonstrated. Consider a coil of wire, a permanent bar magnet and a galvanometer as illustrated in Figures 5.1 and 5.2
eBook - ePub- John C. Slater, Nathaniel H. Frank(Authors)
- 2012(Publication Date)
- Dover Publications(Publisher)
CHAPTER I
THE FIELD THEORY OF ELECTROMAGNETISM
A dynamical problem has two aspects: mechanics, the determination of the accelerations and hence of the motions, once the forces are given; and the study of the forces acting under the existing circumstances. The basic principles of mechanics are simple. In its classical form, mechanics is based on Newton’s laws of motion, laws discovered and formulated nearly three hundred years ago. The developments since then have been technical, mathematical improvements in the way of formulating the laws and solving the resulting mathematical problems, rather than additions to our fundamental knowledge of mechanics. Only in the present century, with wave mechanics, has there been a change in the underlying structure of the subject.The study of forces, on the other hand, is difficult and complex. The first forces brought into mathematical formulation were gravitational forces, as seen in planetary motion. Next were elastic forces. Then followed electric and magnetic forces, which are the subject of this volume. Their study was mostly a product of the nineteenth century. During the present century, it has become clear that electromagnetic forces are of far wider application than was first supposed. It has become evident that, instead of being active only in electrostatic and magnetostatic experiments, and in electromagnetic applications such as the telegraph, dynamo, and radio, the forces between the nuclei and electrons of single atoms, the chemical forces between atoms and molecules, the forces of cohesion and elasticity holding solids together, are all of an electric nature. We might be tempted to generalize and suppose that all forces are electromagnetic, but this appears to be carrying things too far. The prevailing evidence at present indicates that the intranuclear forces, holding together the various fundamental particles of which the nucleus is composed, are not of electromagnetic origin. These forces, of enormous magnitude, and appearing in the phenomena of radioactivity and of nuclear fission, appear subject to laws somewhat analogous to the electromagnetic laws, but fundamentally different. In spite of this, the range of phenomena governed by electromagnetic theory is very wide, and it carries us rather far into the structure of matter, of electrons and nuclei and atoms and molecules, if we wish to understand it completely. The equations underlying the theory, Maxwell’s equations, are relatively simple, but not nearly so simple as Newton’s laws of motion. Instead of stating the whole fundamental formulation of the subject in the first chapter, as one can when dealing with mechanics, about half of the present book is taken up with a complete formulation of Maxwell’s equations. We start with simple types of force, electrostatic and magnetostatic, and gradually work up to problems of electromagnetic induction and related subjects, all of which are formulated in Maxwell’s equations.
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