Physics
Lenz's Law
Lenz's Law states that the direction of an induced electromotive force (emf) in a circuit is always such that it opposes the change in magnetic flux that produced it. This law is based on the principle of conservation of energy and is used to determine the direction of induced currents in electromagnetic phenomena, such as electromagnetic induction and eddy currents.
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9 Key excerpts on "Lenz's Law"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
However, it is usually easier to determine this direction with Lenz’s law, named in honor of its discoverer, Heinrich Lenz (1804–1865). (Faraday also discovered this law, independently of Lenz.) We state Lenz’s law as follows: Lenz’s Law The direction of the induced emf drives current around a wire loop to always oppose the change in magnetic flux that causes the emf. Lenz’s law can also be considered in terms of conservation of energy. If pushing a magnet into a coil causes current, the energy in that current must have come from somewhere. If the induced current causes a magnetic field opposing the increase in field of the magnet we pushed in, then the situation is clear. We pushed a magnet against a field and did work on the system, and that showed up as current. If it were not the case that the induced field opposes the change in the flux, the magnet would be pulled in produce a current without anything having done work. Electric potential energy would have been created, violating the conservation of energy. To determine an induced emf ε , you first calculate the magnetic flux Φ m and then obtain dΦ m /dt. The magnitude of ε is given by ε = | dΦ m /dt | . Finally, you can apply Lenz’s law to determine the sense of ε . This will be developed through examples that illustrate the following problem-solving strategy. Problem-Solving Strategy: Lenz’s Law To use Lenz’s law to determine the directions of induced magnetic fields, currents, and emfs: 1. Make a sketch of the situation for use in visualizing and recording directions. 2. Determine the direction of the applied magnetic field B → . 3. Determine whether its magnetic flux is increasing or decreasing. 4. Now determine the direction of the induced magnetic field B → . The induced magnetic field tries to reinforce a 586 Chapter 13 | Electromagnetic Induction This OpenStax book is available for free at http://cnx.org/content/col12074/1.3 magnetic flux that is decreasing or opposes a magnetic flux that is increasing.
eBook - PDF- Daniel Fleisch(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
This is called Lenz’s law and is discussed later in this chapter. Faraday’s law 59 Here’s an expanded view of the standard form of Faraday’s law: Note that ~ E in this expression is the induced electric field at each segment d ~ l of the path C measured in the reference frame in which that segment is stationary. And here is an expanded view of the alternative form of Faraday’s law: = C d – dl dt E The electric field in V/m Reminder that the electric field is a vector Reminder that this is a line integral (not a surface or a volume integral) An incremental segment of path C Tells you to sum up the contributions from each p ortion of the closed path C in a direction given by the right-hand rule ˆ S da n B Dot product tells you to find the part of E parallel to dl (along path C ) The rate of change with time The magnetic flux through any surface bounded by C ∫ ∫ = C – dl E The electric field in V/m Reminder that the electric field is a vector Dot product tells you to find the part of E parallel to dl (along path C ) Reminder that this is a line integral (not a surface or a volume integral) Tells you to sum up the contributions from each p ortion of the closed path C ˆ S da n The rate of change of the magnetic field with time An incremental segment of path C The flux of the time rate of change of the magnetic field ∫ ∫ A student’s guide to Maxwell’s Equations 60 In this case, ~ E represents the electric field in the laboratory frame of reference (the same frame in which ~ B is measured). Faraday’s law and the flux rule can be used to solve a variety of problems involving changing magnetic flux and induced electric fields, in particular problems of two types: (1) Given information about the changing magnetic flux, find the induced emf. (2) Given the induced emf on a specified path, determine the rate of change of the magnetic field magnitude or direction or the area bounded by the path.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(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. 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). ________________________ WORLD TECHNOLOGIES ________________________ 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.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
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. James Clerk Maxwell drew attention to this fact in his 1861 paper On Physical Lines of Force. In the latter half of part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states: ____________________ WORLD TECHNOLOGIES ____________________ So the flux rule that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both) .... Yet in our explanation of the rule we have used two completely – distinct laws for the two cases for circuit moves and for field changes. We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena. – Richard P. Feynman , The Feynman Lectures on Physics Reflection on this apparent dichotomy was one of the principal paths that led Einstein to develop special relativity: It is known that Maxwell’s electrodynamics—as usually understood at the present time— when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
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. James Clerk Maxwell drew attention to this fact in his 1861 paper On Physical Lines of Force . In the latter half of part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states: ________________________ WORLD TECHNOLOGIES ________________________ So the flux rule that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both) .... Yet in our explanation of the rule we have used two completely – distinct laws for the two cases for circuit moves and for field changes. We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena . – Richard P. Feynman , The Feynman Lectures on Physics Reflection on this apparent dichotomy was one of the principal paths that led Einstein to develop special relativity: It is known that Maxwell’s electrodynamics—as usually understood at the present time— when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- University Publications(Publisher)
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. James Clerk Maxwell drew attention to this fact in his 1861 paper On Physical Lines of Force . In the latter half of part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states: ____________________ WORLD TECHNOLOGIES ____________________ So the flux rule that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both) .... Yet in our explanation of the rule we have used two completely – distinct laws for the two cases for circuit moves and for field changes. We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena . – Richard P. Feynman , The Feynman Lectures on Physics Reflection on this apparent dichotomy was one of the principal paths that led Einstein to develop special relativity: It is known that Maxwell’s electrodynamics—as usually understood at the present time— when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
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. James Clerk Maxwell drew attenti on to this fact in his 1861 paper On Physical Lines of Force . In the latter half of part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states: So the flux rule that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit applies whether the flux changes because the field changes or because the circuit moves (or both) .... Yet in our explanation of the rule we have used two completely – distinct laws for the two cases for circuit moves and for field changes. ________________________ WORLD TECHNOLOGIES ________________________ We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena . – Richard P. Feynman , The Feynman Lectures on Physics Reflection on this apparent dichotomy was one of the principal paths that led Einstein to develop special relativit y: It is known that Maxwell’s electrodynamics—as usually understood at the present time— when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a ma gnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
34-15c. Consider a test charge q 0 moving around the circular path of Fig. 34-15b. The work W done on the charge by the induced electric field in one revolution is q 0 . Equivalently, we can express the work as the electric force q 0 E times the displacement 2 r covered in one revolution. Setting these E B E B , E B E B d B B /dt d B B /dt. B B , E B two expressions for W equal to one another and canceling the factor q 0 , we obtain (34-11) The right side of Eq. 34-11 can be expressed as a line inte- gral of around the circle, which can be written in more general cases (for instance, when is not constant or when the chosen closed path is not a circle) as (34-12) Note that Eq. 34-12 reduces directly to Eq. 34-11 in our special case of a circular path with constant tangential Replacing the emf by Eq. 34-12, we can write Faraday’s law of induction ( d B /dt ) as (34-13) It is in this form that Faraday’s law appears as one of the four basic Maxwell equations of electromagnetism. In this form, it is apparent that Faraday’s law implies that a chang- ing magnetic field produces an electric field. The direction of the line integral is related to the direction of in B by the same right-hand rule discussed at the end of Section 34- 3: with the fingers in the direction of around the closed integration path, the thumb indicates the direction of In Fig. 34-15, we have assumed that the magnetic field is increasing; that is, both dB/dt and d B /dt are positive. By Lenz’ law, the induced emf opposes this change, and thus the induced currents create a magnetic field that points out of the plane of the figure. Since the currents must be counterclock- wise, the lines of induced electric field (which is responsi- ble for the current) must also be counterclockwise. If, on the other hand, the magnetic field were decreasing (dB/dt 0), the lines of induced electric field would be clockwise, such that the induced current again opposes the change in B .
eBook - PDF- Saad Osman Bashir(Author)
- 2015(Publication Date)
- IntechOpen(Publisher)
Chapter 3 The Electromagnetic Force between Two Parallel Current Conductors Explained Using Coulomb’s Law Jan Olof Jonson Additional information is available at the end of the chapter http://dx.doi.org/10.5772/61221 Abstract In this book chapter the electromagnetic force between two parallel electric conduc‐ tors has been derived, applying thereby the effects of propagation delay and the Spe‐ cial Relativity theory, taking thereby also into count the thus far neglected effects introduced by the voltage sources of both circuits. This has been done for a specific case consisting of two rectangular circuits, aligned to each other along one of the long sides, at a distance that is short compared to the long sides. The intention in doing so is to make a meaningful application of the concept of “two parallel conductors of in‐ finite length”, so that it is possible to make a complete calculation of the force between the two circuits, avoiding thus making a vague claim as for example Maxwell, saying that the other parts of the conductors do not contribute to the force. What is radically new in this interpretation is that it is Coulomb’s law that is responsible for the force. Keywords: Ampère’s Bridge, Ampère’s Law, Coulomb’s Law, electromagnetic force, Lorentz force, Lorentz transformation, parallel conductors, propagation delay, retard‐ ed action, Special Relativity theory, Sagnac effect, time dilatation 1. Introduction In several papers evidence has been presented that is able to refute the widely recognized electromagnetic theory of today [1-5]. One such fundamental law is Lorentz’ force law. Already 1997 a paper presented mathematical proofs showing that this law is unable to explain the repulsive force between collinear currents, demonstrated in the case of Ampère’s bridge [1]. Even Graneau’s exploding wires and Hering’s pump cause difficulties, when trying to use Lorentz’ force law in order to explain the effects that have been registered [6-11].
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