Lenz's law

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Lenz's law tells the direction of a current in a conductor loop induced indirectly by the change in magnetic flux through the loop. Scenarios a, b, c, d and e are possible. Scenario f is impossible due to the law of conservation of energy. The charges (electrons) in the conductor are not pushed in motion directly by the change in flux, but by a circular electric field (not pictured) surrounding the total magnetic field of inducing and induced magnetic fields. This total magnetic field induces the electric field. Lenz law demonstration.png
Lenz's law tells the direction of a current in a conductor loop induced indirectly by the change in magnetic flux through the loop. Scenarios a, b, c, d and e are possible. Scenario f is impossible due to the law of conservation of energy. The charges (electrons) in the conductor are not pushed in motion directly by the change in flux, but by a circular electric field (not pictured) surrounding the total magnetic field of inducing and induced magnetic fields. This total magnetic field induces the electric field.

Lenz's law, named after the physicist Emil Lenz (pronounced /ˈlɛnts/ ) who formulated it in 1834, [1] states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.

Physicist scientist who does research in physics

A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies.

Emil Lenz Russian physicist

Heinrich Friedrich Emil Lenz, usually cited as Emil Lenz, was a Russian physicist of Baltic German ethnicity. He is most noted for formulating Lenz's law in electrodynamics in 1834.

Magnetic field spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. The effects of magnetic fields are commonly seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. They exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location. As such, it is described mathematically as a vector field.

Contents

It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or the drag force of eddy currents exerted on moving objects in a magnetic field.

Electromagnetism Branch of science concerned with the phenomena of electricity and magnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, is responsible for electromagnetic radiation such as light, and is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Inductor Passive two-terminal electrical component that stores energy in its magnetic field

An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil around a core.

Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material. When graphed, these circular currents within a piece of metal look vaguely like eddies or whirlpools in a liquid.

Lenz's law may be seen as analogous to Newton's third law in classic mechanics. [2]

Definition

Lenz's law states that the current induced in a circuit due to a change or a motion in a magnetic field is so directed as to oppose the change in flux and to exert a mechanical force opposing the motion.

Lenz's law is contained in the rigorous treatment of Faraday's law of induction, where it finds expression by the negative sign:

Faradays law of induction Basic law of electromagnetism of magnetic fields inducing a potential difference

Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.

which indicates that the induced electromotive force and the rate of change in magnetic flux have opposite signs. [3]

Electromotive force scalar physical quantity

Electromotive force, abbreviated emf, is the electrical action produced by a non-electrical source. A device that converts other forms of energy into electrical energy, such as a battery or generator, provides an emf as its output. Sometimes an analogy to water "pressure" is used to describe electromotive force.

Magnetic flux physical quantity

In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the measurement of magnetic flux.

This means that the direction of the back EMF of an induced field opposes the changing current that is its cause. D.J. Griffiths summarized it as follows: Nature abhors a change in flux. [4]

David J. Griffiths American physicist and textbook author

David Jeffrey Griffiths is a U.S. physicist and educator. He worked at Reed College from 1978 through 2009, becoming the Howard Vollum Professor of Science before his retirement. He is not to be confused with the late physicist David J. Griffiths of Oregon State University.

If a change in the magnetic field of current i1 induces another electric current, i2, the direction of i2 is opposite that of the change in i1. If these currents are in two coaxial circular conductors 1 and 2 respectively, and both are initially 0, then the currents i1 and i2 must counter-rotate. The opposing currents will repel each other as a result.

Example

Currents bound inside the atoms of strong magnets can create counter-rotating currents in a copper or aluminum pipe. This is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe.

When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the flux is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to oppose the change.

Detailed interaction of charges in these currents

Aluminium ring moved by electromagnetic induction, thus demonstrating Lenz's law.
Experiment showing Lenz's law with two aluminium rings on a scales-like device set up on a pivot so as to freely move in the horizontal plane. One ring is fully enclosed, while the other has an opening, not forming a complete circle. When we place a bar magnet near the fully enclosed ring, the ring is repulsed by it. However, when the system comes to a rest, and we remove the bar magnet, then the ring is attracted by it. In the first case, the induced current created in the ring resists the increase of magnetic flux caused by the proximity of the magnet, while in the latter, taking the magnet out of the ring decreases the magnetic flux, inducing such current whose magnetic field resists the decrease of flux. This phenomenon is absent when we repeat the experiment with the ring that isn't enclosed by inserting and removing the magnet bar. The induced currents in this ring can't enclose themselves in the ring, and have a very weak field that cannot resist the change of the magnetic flux.

In electromagnetism, when charges move along electric field lines work is done on them, whether it involves storing potential energy (negative work) or increasing kinetic energy (positive work).

When net positive work is applied to a charge q1, it gains speed and momentum. The net work on q1 thereby generates a magnetic field whose strength (in units of magnetic flux density (1 tesla = 1 volt-second per square meter)) is proportional to the speed increase of q1. This magnetic field can interact with a neighboring charge q2, passing on this momentum to it, and in return, q1 loses momentum.

The charge q2 can also act on q1 in a similar manner, by which it returns some of the momentum that it received from q1. This back-and-forth component of momentum contributes to magnetic inductance. The closer that q1 and q2 are, the greater the effect. When q2 is inside a conductive medium such as a thick slab made of copper or aluminum, it more readily responds to the force applied to it by q1. The energy of q1 is not instantly consumed as heat generated by the current of q2 but is also stored in two opposing magnetic fields. The energy density of magnetic fields tends to vary with the square of the magnetic field's intensity; however, in the case of magnetically non-linear materials such as ferromagnets and superconductors, this relationship breaks down.

Conservation of momentum

Momentum must be conserved in the process, so if q1 is pushed in one direction, then q2 ought to be pushed in the other direction by the same force at the same time. However, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced (see retarded potential). This means that for a brief period the total momentum of the two charges is not conserved, implying that the difference should be accounted for by momentum in the fields, as asserted by Richard P. Feynman. [5] Famous 19th century electrodynamicist James Clerk Maxwell called this the "electromagnetic momentum". [6] Yet, such a treatment of fields may be necessary when Lenz's law is applied to opposite charges. It is normally assumed that the charges in question have the same sign. If they do not, such as a proton and an electron, the interaction is different. An electron generating a magnetic field would generate an EMF that causes a proton to accelerate in the same direction as the electron. At first, this might seem to violate the law of conservation of momentum, but such an interaction is seen to conserve momentum if the momentum of electromagnetic fields is taken into account.

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A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.

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Counter-electromotive force, also known as back electromotive force, is the electromotive force or "voltage" that opposes the change in current which induced it. CEMF is the EMF caused by magnetic induction.

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The search coil magnetometer or induction magnetometer, based on an inductive sensor, is a magnetometer which measures the varying magnetic flux due to Lenz's law. An inductive sensor connected to a conditioning electronic circuit constitutes a search coil magnetometer. It is a vector magnetometer which can measure one or more components of the magnetic field. A classical configuration uses three orthogonal inductive sensors. The search-coil magnetometer can measure magnetic field from mHz up to hundreds of MHz.

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References

  1. Lenz, E. (1834), "Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme", Annalen der Physik und Chemie, 107 (31), pp. 483–494. A partial translation of the paper is available in Magie, W. M. (1963), A Source Book in Physics, Harvard: Cambridge MA, pp. 511–513.
  2. Schmitt, Ron. Electromagnetics explained. 2002. Retrieved 16 July 2010.
  3. Giancoli, Douglas C. (1998). Physics: principles with applications (5th ed.). p. 624.
  4. Griffiths, David. Introduction to Electrodynamics. p. 315. ISBN   978-0-321-85656-2.
  5. The Feynman Lectures on Physics : Volume I, Chapter 10, page 9.
  6. Maxwell, James C. A treatise on electricity and magnetism, Volume 2. Retrieved 16 July 2010.