Physics
Changing Magnetic Field
A changing magnetic field refers to a magnetic field that is in the process of increasing or decreasing in strength or direction over time. This change can induce an electric current in a nearby conductor, as described by Faraday's law of electromagnetic induction. It is a fundamental concept in electromagnetism and is widely used in various technologies such as generators and transformers.
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10 Key excerpts on "Changing Magnetic Field"
eBook - PDF- Anthony Wolbarst(Author)
- 2005(Publication Date)
- Medical Physics Publishing(Publisher)
Both of these phenomena play critically important roles in MRI. 3. A Changing Magnetic Field Produces an Electric Field, and a Changing Electric Field Produces a Magnetic Field In 1831, Michael Faraday reported a third fundamental process linking electricity and magnetism: when the current in one wire is abruptly changed, a brief current is induced in another, nearby conductor. More generally, a Changing Magnetic Field gives rise to a transient electric field in the surrounding space. The classic demonstration of this electromagnetic induction is to drop a bar magnet through a loop of wire that includes an ammeter or voltmeter (Figure 6–3a). As the magnet passes through the loop, the resulting brief pulse of voltage and electric field within the wire drives a pulse of current around it, first one way and then the other (because the two poles drive the electrons in opposite directions as they pass by), and the meter pointer swings back and forth. The world’s simplest electric generator. Guided by the discovery of electromagnetic induction, James Clerk Maxwell postulated the existence of a fourth basic phenomenon, the converse of magnetic induction, in which a changing electric field gives rise to a transient magnetic field. The reality of this effect, too, can be demonstrated by experi- ment (Figure 6–3b). The stage was now set for one of the great scientific leaps of imagination—Maxwell’s explanation of electromagnetic radiation. Inductor But before going there, let us return briefly to Figure 6–3a, and explore magnetic induction a little more. Certain materials become superconductors below very low temperatures (near absolute zero), as we shall see in chapter 9. In that state, they offer literally zero electrical resistance. If we replaced the normal wire in the figure with one that is super- conducting, the circuit could then pass an electric current indefinitely.
eBook - PDF- Edward Purcell(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
6.1 Definition of the Magnetic Field 6.2 Some Properties of the Magnetic Field 6.3 Vector Potential 6.4 Field of Any Current-Carrying Wire 6.5 Fields of Rings and Coils 6.6 Change in B at a Current Sheet 6.7 How the Fields Transform 6.8 Rowland's Experiment 6.9 Electric Conduction in a Magnetic Field: The Hall Effect Problems THE MAGNETIC FIELD 208 214 220 223 226 231 235 241 241 245 208 CHAPTER SIX DEFINITION OF THE MAGNETIC FIELD 6.1 A charge which is moving parallel to a current of other charges experiences a force perpendicular to its own velocity. We can see it happening in the deflection of the electron beam in Fig. 5.3. We dis- covered in Section 5.9 that this is consistent with-indeed, is required by-Coulomb's law with charge invariance and special relativity. And we found that a force perpendicular to the charged particle's velocity also arises in motion at right angles to the current-carrying wire. For a given current the magnitude of the force, which we calculated for the particular case in Fig. 5.20a, is proportional to the product of the particle's charge q and its speed v in our frame. Just as we defined the electric field E as the vector force on unit charge at rest, so we can define another field B by the velocity-dependent part of the force that acts on a charge in motion. The defining relation was introduced at the beginning of Chapter 5. Let us state it again more carefully. At some instant t a particle of charge q passes the point (x, y, z) in our frame, moving with velocity v. At that moment the force on the particle (its rate of change of momentum) is F. The electric field at that time and place is known to be E. Then the magnetic field at that time and place is defined as the vector B which satisfies the vector equation F = qE + 1v X B c (1) Of course, F here includes only the charge-dependent force and not, for instance, the weight of the particle carrying the charge.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
An electric field is a field created by an electric charge and such fields are intimately related to magnetic fields; a Changing Magnetic Field generates an electric field and a changing electric field produces a magnetic field. The full relationship between the electric and magnetic fields, and the currents and charges that create them, is described by the set of Maxwell's equations. In view of special relativity, electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic field. A pure electric field in one reference frame is observed as a combination of both an electric field and a magnetic field in a moving reference frame. In quantum physics, this electromagnetic field is understood to be caused by virtual photons. Most often this quantum description is not needed because the simpler classical theory is sufficient. ________________________ WORLD TECHNOLOGIES ________________________ Magnetic fields have had many uses in ancient and modern society. The Earth produces its own magnetic field, which is important in navigation since the north pole of a compass points toward the south pole of Earth's magnetic field, located near the Earth's geographical north. Rotating magnetic fields are utilized in both electric motors and generators. Magnetic forces give information about the charge carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. History One of the first drawings of a magnetic field, by René Descartes, 1644. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, threaded parts, through threaded pores in magnets. Although magnets and magnetism were known much earlier, one of the first descriptions of the magnetic field was produced in 1269 C.E.
eBook - PDF- Daniel Fleisch(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
3 Faraday’s law In a series of epoch-making experiments in 1831, Michael Faraday demonstrated that an electric current may be induced in a circuit by changing the magnetic flux enclosed by the circuit. That discovery is made even more useful when extended to the general statement that a Changing Magnetic Field produces an electric field. Such ‘‘induced’’ elec-tric fields are very different from the fields produced by electric charge, and Faraday’s law of induction is the key to understanding their behavior. 3.1 The integral form of Faraday’s law In many texts, the integral form of Faraday’s law is written as I C ~ E d ~ l ¼ d dt Z S ~ B ^ n da Faraday ’ s law ð integral form Þ : Some authors feel that this form is misleading because it confounds two distinct phenomena: magnetic induction (involving a Changing Magnetic Field) and motional electromotive force (emf) (involving movement of a charged particle through a magnetic field). In both cases, an emf is produced, but only magnetic induction leads to a circulating electric field in the rest frame of the laboratory. This means that this common version of Faraday’s law is rigorously correct only with the caveat that ~ E rep-resents the electric field in the rest frame of each segment d ~ l of the path of integration. 58 A version of Faraday’s law that separates the two effects and makes clear the connection between electric field circulation and a Changing Magnetic Field is emf ¼ d dt Z S ~ B ^ n da Flux rule , I C ~ E d ~ l ¼ Z S @ ~ B @ t ^ n da Faraday ’ s law ð alternate form Þ : Note that in this version of Faraday’s law the time derivative operates only on the magnetic field rather than on the magnetic flux, and both ~ E and ~ B are measured in the laboratory reference frame. Don’t worry if you’re uncertain of exactly what emf is or how it is related to the electric field; that’s all explained in this chapter.
eBook - PDF- Bhag Singh Guru, Hüseyin R. Hiziroglu(Authors)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
An electromagnet creates a time-varying magnetic field, and the gap between the pole faces of the electromagnet increases radially outward to control the strength of the magnetic field as shown in Figure 7.28. Let us assume that a charged particle (an electron) is at rest, and the magnetic field is zero. As the magnetic field increases in the z direction, it induces an electric field, Figure 7.29, which forms closed circular loops in the plane of the torus. The electric field intensity, from Maxwell’s equation, is c E · d = − s ∂ B ∂ t · d s 335 7.14 Applications of electromagnetic fields Figure 7.28 Schematic of a betatron Figure 7.29 Forces experienced by an electron revolving with a velocity u at radius ρ where B ( r , t ), the magnetic flux density, is a function of space and time. The symmetric design of the electromagnet ensures that the magnitude of the B field is the same at a constant radius from the center. Thus, at the same radius, the strength of the E field is also constant. Thus, for a loop of constant radius a , the preceding equation yields E φ = − 1 2 π a d dt (7.145) where = a 0 B ρ d ρ 2 π 0 d φ (7.146) is the total flux passing through the surface bounded by the circular loop of radius a . The force exerted by the E field on the electron is F φ = − eE φ = e 2 π a d dt (7.147) where e is the magnitude of the charge on the electron (1 . 602 × 10 − 19 C). According to Newton’s second law of motion, the rate of change of momentum is equal to the impressed force. That is dp dt = e 2 π a d dt The electron is at rest at t = 0 ; therefore, the gain in momentum at any time t is p = e 2 π a (7.148) As soon as the electron starts revolving in the circular path at a radial distance a from the center, it experiences the Lorentz force, − e ( u × B ). This force tends to move the electron toward its center as indicated in 336 7 Time-varying electromagnetic fields Figure 7.29.
eBook - PDFEngineering Electromagnetics
Pergamon Unified Engineering Series
- David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
(9.10) Moving Electromagnetic Fields 291 The physical interpretation of this result is as earlier stated-the moving charge sees an electric field, E', given above and different from that measured by a stationery observer. Likewise, the force measured on the moving charge is F = <7[E + vXB]. Example 1 -Voltage Induced by a Moving Wire How do these transformed fields tell us the induced voltage? Consider the rectangular circuit of conductors shown in Fig. 9-2. Fig. 9-2. Conductor moving in magnetic field. The rectangular array of copper wires shown above is fixed except for the wire conductor connecting points A and B which slides to the right with velocity, v. The circuit A BCD is never broken. The copper wires have resistance per meter, r. In addition to the moving wire, a uniform magnetic field, B 0 , is directed into the paper as shown. Under these conditions: (a) How much voltage is induced in circuit ABC D and where is it induced? (b) How much current flows in circuit ABCD and in what direction? Our new found fields on moving bodies will permit us to solve this problem. First, define two systems of coordinates as before: one fixed with the wires, and two moving on the moving bar/4Z?. The coordinate origins are fixed on the lower bar CB. In the fixed coordinates (x,y, z or unprimed) the fields are (9.11) From our transformation equations just derived, the fields in the moving system as experienced on the bar are E' = E + vxB = 0+(jfo>) X (-¿B 0 ), (9 12 ) E'=+yB 0 v, 292 Time-Varying Fields and of course B ' = B = -zB 0 . How does this relate to induced voltage? In electrostatics, we defined voltage as (9.13) The voltage (potential difference) between points B and^4 is vB 0 h, with point A at the higher potential. Is it correct to use the same definition of voltage for time-varying fields as for electrostatics? It must be because everyone does so! How-ever, voltage now may depend on the path chosen in the integration.
eBook - PDF- John A. Jacobs(Author)
- 1987(Publication Date)
- Academic Press(Publisher)
Chapter Four The Earth‘s Magnetic Field 4.1 Introduction At its strongest near the poles the Earth’s magnetic field is several hundred times weaker than that between the poles of a toy horseshoe magnet-being less than a gauss (r). Thus, in geomagnetic studies we are measuring extremely small magnetic fields and a more convenient unit is the gamma (y), defined as lO-’r. Strictly speaking the unit of magnetic field strength is the oersted, the gauss being the unit of magnetic induction. The distinction is somewhat pedantic in geophysical applications since the permeability of air is virtually unity in cgs units. In SI units, which will be used here, l r = Wbm-2 (Weber/m2) = T (tesla). Thus, l y = 10-9T = In T. The magnetic field at any point on the Earth’s surface may be specified by three parameters, e.g. the total intensity F, declination D and inclination I or the two horizontal components X and Y and the vertical component 2. Simple relationships exist between these different magnetic elements (see e.g. Jacobs, 1966). The variation of the magnetic field over the Earth’s surface is best illustrated by isomagnetic charts, i.e. maps on which lines are drawn through points at which a given magnetic element has the same value. Con- tours of equal intensity in any of the elements X , Y, Z , H or F are called iso- dynamics. Figures 4.1 and 4.2 are world maps showing contours of equal declination (isogonics) and equal inclination (isoclinics) for the year 1985. It is remarkable that a phenomenon (the Earth’s magnetic field) whose origin, as we shall see later, lies within the Earth should show so little relation to the broad features of geology and geography. 191 192 The Earths Core Not only do the intensity and direction of magnetization vary from place to place across the Earth, but they also show a time variation. There are two distinct types of temporal changes: transient fluctuations and long-term secu- lar changes.
eBook - ePub- Branislav M. Notaroš(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
TIME-VARYING ELECTROMAGNETIC FIELD IntroductionWe now introduce time variation of electric and magnetic fields into our electromagnetic model. The new field is the time-varying electromagnetic field, which is caused by time-varying charges and currents. As opposed to static fields, the electric and magnetic fields constituting the time-varying electromagnetic field are coupled to each other and cannot be analyzed separately. Moreover, the mutual induction (generation) of time-varying electric and magnetic fields is the basis of propagation of electromagnetic waves and of electromagnetic radiation. The first essentially new feature that is not present under the static assumption is electromagnetic induction, where we also study the related concept of inductance. The other crucial step is addition of a new type of current, so-called displacement current, to the static version of the generalized Ampère’s law. The full set of general Maxwell’s equations – in integral and differential notation, and in the form of boundary conditions – is studied and used in the time domain, as well as in the complex (frequency) domain, which is usually considerably more efficient. The time retardation (lagging in time of fields behind their sources) is quantified and Lorenz (retarded) electromagnetic potentials are introduced and evaluated. The chapter also discusses Poynting’s theorem, as an expression of the principle of conservation of energy for electromagnetic phenomena.6.1 Induced Electric Field Intensity VectorWe know from Chapter 1 that a point charge Q in free space is a source of an electric field, predicted by Coulomb’s law and described by Eq. (1.4 ). On the other side, the Biot–Savart law (Chapter 4 ) tells us that there will also be a magnetic field, given by Eq. (4.4 ), if this charge moves with some velocity v in space. We now introduce a third field, which will exist in the space around the charge whenever the velocity v changes in time, i.e., whenever the acceleration (or deceleration) a = dv/dt
eBook - ePubElectromagnetics Explained
A Handbook for Wireless/ RF, EMC, and High-Speed Electronics
- Ron Schmitt(Author)
- 2002(Publication Date)
- Newnes(Publisher)
(The DC magnetic field can be supplied by permanent magnets or by an electromagnet.) With a DC field applied, ferrites become anisotropic; that is, their magnetic properties are different in different directions. Simply stated, the DC field causes the ferrite to be saturated in the direction of the field while remaining unsaturated in the other two directions. Voltage-controlled phase-shifters and filters as well as exotic directional devices such as gyrators, isolators, and circulators can be created with ferrites in the microwave region. MAXWELL’S EQUATIONS AND THE DISPLACEMENT CURRENT In the 1860s, the British physicist James Clerk Maxwell set himself to the task of completely and concisely writing all the known laws of electricity and magnetism. During this exercise, Maxwell noticed a mathematical inconsistency in Ampere’s law. Recall that Ampere’s law predicts that a magnetic field surrounds all electric currents. To fix the problem, Maxwell proposed that not only do electric currents, the movement of charge, produce magnetic fields, but changing electric fields also produce magnetic fields. In other words, you do not necessarily need a charge to produce a magnetic field. For instance, when a capacitor is charging, there exists a changing electric field between the two plates. When an AC voltage is applied to a capacitor, the constant charging and discharging leads to current going to and from the plates. As I discussed in Chapter 1, although no current ever travels between the plates, the storing of opposite charges on the plates gives the perceived effect of a current traveling through the capacitor. This virtual current is called displacement current, named so because the virtual current arises from the displacement of charge at the plates
eBook - ePub- (Author)
- 2008(Publication Date)
- Elsevier Science(Publisher)
Chapter 1 Magnetic Field in a Nonmagnetic MediumAlex A. Kaufman, Richard O. Hansen, Robert L.K. KleinbergAbstractPublisher SummaryThis chapter focuses on the magnetic field in a nonmagnetic medium. Numerous experiments performed at the beginning of the19th century demonstrated that constant currents interact with each other that mean mechanical forces act at every element of the circuit. Certainly, this is one of the amazing phenomena of the nature and would have been very difficult to predict. In fact, it is almost impossible to expect that the motion of electrons inside of wire may cause a force on moving charges somewhere else, for instance, in another wire with current, and for this reason the phenomenon of this interaction was discovered by chance. By analogy with the attraction field caused by masses, it is proper to assume that constant (time-invariant) currents create a field and because of the existence of this field and of the existence of this field, other current elements experience the action of the force F. Such a field is called the magnetic field, and it can be introduced from Ampere’s law.1.1 Interaction of constant currents and Ampere's law
Numerous experiments performed at the beginning of the19th century demonstrated that constant currents interact with each other; that is mechanical forces act at every element of the circuit. Certainly, this is one of the amazing phenomena of the nature and would have been very difficult to predict. In fact, it is almost impossible to expect that the motion of electrons inside of wire may cause a force on moving charges somewhere else, for instance, in another wire with current, and for this reason the phenomenon of this interaction was discovered by chance. It turns out that this force of interaction between currents in two circuits depends on the magnitude of these currents, the direction of charge movement, the shape and dimensions of circuits, as well as the their mutual position with respect to each other. The list of factors clearly shows that the mathematical formulation of the interaction of currents should be much more complicated task than that for masses or electric charges. In spite of this fact, Ampere was able to find a relatively simple expression for the force of the interaction of so-called elementary currents:
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