Electromagnetic induction

Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.

Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.

Induction experiment
Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current that 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).[1]


Faraday emf experiment
A diagram of Faraday's iron ring apparatus. Change in the magnetic flux of the left coil induces a current in the right coil.[2]
Faraday disk generator
Faraday's disk (see homopolar generator)

Electromagnetic induction was discovered by Michael Faraday, published in 1831.[3][4] It was discovered independently by Joseph Henry in 1832.[5][6]

In Faraday's first experimental demonstration (August 29, 1831), he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his understanding of electromagnets, he expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. He saw a transient current, which he called a "wave of electricity", when he connected the wire to the battery and another when he disconnected it.[7] This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected.[2] Within two months, Faraday found several other manifestations of electromagnetic induction. 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 the bar magnet with a sliding electrical lead ("Faraday's disk").[8]

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.[9] An exception was James Clerk Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory.[9][10][11] In Maxwell's model, 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 from Faraday's original formulation and does not describe motional EMF. Heaviside's version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations.

In 1834 Heinrich Lenz formulated the law named after him to describe the "flux through the circuit". Lenz's law gives the direction of the induced EMF and current resulting from electromagnetic induction.


Faraday's law of induction and Lenz's law

A solenoid
VFPt Solenoid correct2
The longitudinal cross section of a solenoid with a constant electrical current running through it. The magnetic field lines are indicated, with their direction shown by arrows. The magnetic flux corresponds to the 'density of field lines'. The magnetic flux is thus densest in the middle of the solenoid, and weakest outside of it.

Faraday's law of induction makes use of the magnetic flux ΦB through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral:[12]

where dA is an element of the surface Σ enclosed by the wire loop, B is the magnetic field. The dot product B·dA corresponds to an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.

When the flux through the surface changes, Faraday's law of induction says that the wire loop acquires an electromotive force (EMF).[note 1] The most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit:[16][17]


where is the EMF and ΦB is the magnetic flux. The direction of the electromotive force is given by Lenz's law which states that an induced current will flow in the direction that will oppose the change which produced it.[18] This is due to the negative sign in the previous equation. To increase the generated EMF, a common approach is to exploit flux linkage by creating a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them. The resulting EMF is then N times that of one single wire.[19][20]

Generating an EMF through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways:

  1. the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger),
  2. the wire loop is deformed and the surface Σ changes,
  3. the orientation of the surface dA changes (e.g. spinning a wire loop into a fixed magnetic field),
  4. any combination of the above

Maxwell–Faraday equation

In general, the relation between the EMF in a wire loop encircling a surface Σ, and the electric field E in the wire is given by

where d is an element of contour of the surface Σ, combining this with the definition of flux

we can write the integral form of the Maxwell–Faraday equation

It is one of the four Maxwell's equations, and therefore plays a fundamental role in the theory of classical electromagnetism.

Faraday's law and relativity

Faraday's law describes two different phenomena: the motional EMF generated by a magnetic force on a moving wire (see Lorentz force), and the transformer EMF this is generated by an electric force due to a changing magnetic field (due to the differential form of the Maxwell–Faraday equation). James Clerk Maxwell drew attention to the separate physical phenomena in 1861.[21][22] This is believed to be a unique example in physics of where such a fundamental law is invoked to explain two such different phenomena.[23]

Einstein noticed that the two situations both corresponded to a relative movement between a conductor and a magnet, and the outcome was unaffected by which one was moving. This was one of the principal paths that led him to develop special relativity.[24]


The principles of electromagnetic induction are applied in many devices and systems, including:

Electrical generator

Rectangular wire loop rotating at angular velocity ω in radially outward pointing magnetic field B of fixed magnitude. The circuit is completed by brushes making sliding contact with top and bottom discs, which have conducting rims. This is a simplified version of the drum generator.

The EMF generated by Faraday's law of induction due to relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created. If the wire is connected through an electrical load, current will flow, and thus electrical energy is generated, converting the mechanical energy of motion to electrical energy. For example, the drum generator is based upon the figure to the bottom-right. A different implementation of this idea is the Faraday's disc, shown in simplified form on the right.

In the Faraday's disc example, the disc is rotated in a uniform magnetic field perpendicular to the disc, causing a current to flow in the radial arm due to the Lorentz force. Mechanical work is necessary to drive this current. When the generated current flows through the conducting rim, a magnetic field is generated by this current through Ampère's circuital law (labelled "induced B" in the figure). The rim thus becomes an electromagnet that resists rotation of the disc (an example of Lenz's law). On the far side of the figure, the return current flows from the rotating arm through the far side of the rim to the bottom brush. The B-field induced by this return current opposes the applied B-field, tending to decrease the flux through that side of the circuit, opposing the increase in flux due to rotation. On the near side of the figure, the return current flows from the rotating arm through the near side of the rim to the bottom brush. The induced B-field increases the flux on this side of the circuit, opposing the decrease in flux due to rotation. Thus, both sides of the circuit generate an EMF opposing the rotation. The energy required to keep the disc moving, despite this reactive force, is exactly equal to the electrical energy generated (plus energy wasted due to friction, Joule heating, and other inefficiencies). This behavior is common to all generators converting mechanical energy to electrical energy.

Electrical transformer

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, d ΦB / 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.

Current clamp

Current Clamp
A current clamp

A current clamp is a type of transformer with a split core which can be spread apart and clipped onto a wire or coil to either measure the current in it or, in reverse, to induce a voltage. Unlike conventional instruments the clamp does not make electrical contact with the conductor or require it to be disconnected during attachment of the clamp.

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.

Eddy currents

Conductors (of finite dimensions) moving through a uniform magnetic field, or stationary within a changing magnetic field, will have currents induced within them. These induced eddy currents can be undesirable, since they dissipate energy in the resistance of the conductor. There are a number of methods employed to control these undesirable inductive effects.

  • Electromagnets in electric motors, generators, and transformers do not use solid metal, but instead use thin sheets of metal plate, called laminations. These thin plates reduce the parasitic eddy currents, as described below.
  • Inductive coils in electronics typically use magnetic cores to minimize parasitic current flow. They are a mixture of metal powder plus a resin binder that can hold any shape. The binder prevents parasitic current flow through the powdered metal.

Electromagnet laminations

Hawkins Electrical Guide - Figure 292 - Eddy currents in a solid armature

Eddy currents occur when a solid metallic mass is rotated in a magnetic field, because the outer portion of the metal cuts more lines of force than the inner portion, hence the induced electromotive force not being uniform, tends to set up currents between the points of greatest and least potential. Eddy currents consume a considerable amount of energy and often cause a harmful rise in temperature.[25]

Hawkins Electrical Guide - Figure 293 - Armature core with a few laminations showing effect on eddy currents

Only five laminations or plates are shown in this example, so as to show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 to 66 per inch, and brings the eddy current loss down to about one percent. While the plates can be separated by insulation, the voltage is so low that the natural rust/oxide coating of the plates is enough to prevent current flow across the laminations.[25]

Small DC Motor pole laminations and overview

This is a rotor approximately 20mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used to limit parasitic inductive losses.

Parasitic induction within conductors

Hawkins Electrical Guide - Figure 291 - Formation of eddy currents in a solid bar inductor

In this illustration, a solid copper bar conductor on a rotating armature is just passing under the tip of the pole piece N of the field magnet. Note the uneven distribution of the lines of force across the copper bar. The magnetic field is more concentrated and thus stronger on the left edge of the copper bar (a,b) while the field is weaker on the right edge (c,d). Since the two edges of the bar move with the same velocity, this difference in field strength across the bar creates whorls or current eddies within the copper bar.[25]

High current power-frequency devices, such as electric motors, generators and transformers, use multiple small conductors in parallel to break up the eddy flows that can form within large solid conductors. The same principle is applied to transformers used at higher than power frequency, for example, those used in switch-mode power supplies and the intermediate frequency coupling transformers of radio receivers.

See also



  1. ^ The EMF is the voltage that would be measured by cutting the wire to create an open circuit, and attaching a voltmeter to the leads. Mathematically, is defined as the energy available from a unit charge that has traveled once around the wire loop.[13][14][15]


  1. ^ Poyser, A. W. (1892). Magnetism and Electricity: A Manual for Students in Advanced Classes. London and New York: Longmans, Green, & Co. p. 285.
  2. ^ a b Giancoli, Douglas C. (1998). Physics: Principles with Applications (Fifth ed.). pp. 623–624.
  3. ^ Ulaby, Fawwaz (2007). Fundamentals of applied electromagnetics (5th ed.). Pearson:Prentice Hall. p. 255. ISBN 0-13-241326-4.
  4. ^ "Joseph Henry". Distinguished Members Gallery, National Academy of Sciences. Archived from the original on 2013-12-13. Retrieved 2006-11-30.
  5. ^ "A Brief History of Electromagnetism" (PDF).
  6. ^ "Electromagnetism". Smithsonian Institution Archives.
  7. ^ Michael Faraday, by L. Pearce Williams, p. 182-3
  8. ^ Michael Faraday, by L. Pearce Williams, p. 191–5
  9. ^ a b Michael Faraday, by L. Pearce Williams, p. 510
  10. ^ Maxwell, James Clerk (1904), A Treatise on Electricity and Magnetism, Vol. II, Third Edition. Oxford University Press, pp. 178–9 and 189.
  11. ^ "Archives Biographies: Michael Faraday", The Institution of Engineering and Technology.
  12. ^ Good, R. H. (1999). Classical Electromagnetism. Saunders College Publishing. p. 107. ISBN 0-03-022353-9.
  13. ^ Feynman, R. P.; Leighton, R. B.; Sands, M. L. (2006). The Feynman Lectures on Physics, Volume 2. Pearson/Addison-Wesley. pp. 17–2. ISBN 0-8053-9049-9.
  14. ^ Griffiths, D. J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. pp. 301–303. ISBN 0-13-805326-X.
  15. ^ Tipler, P. A.; Mosca, G. (2003). Physics for Scientists and Engineers (5th ed.). W.H. Freeman. p. 795. ISBN 978-0716708100.
  16. ^ Jordan, E.; Balmain, K. G. (1968). Electromagnetic Waves and Radiating Systems (2nd ed.). Prentice-Hall. p. 100.
  17. ^ Hayt, W. (1989). Engineering Electromagnetics (5th ed.). McGraw-Hill. p. 312. ISBN 0-07-027406-1.
  18. ^ Schmitt, R. (2002). Electromagnetics Explained. p. 75.
  19. ^ Whelan, P. M.; Hodgeson, M. J. (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1.
  20. ^ Nave, C. R. "Faraday's Law". HyperPhysics. Georgia State University. Retrieved 2011-08-29.
  21. ^ Maxwell, J. C. (1861). "On physical lines of force". Philosophical Magazine. 90: 11–23. doi:10.1080/1478643100365918.
  22. ^ Griffiths, D. J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. pp. 301–303. ISBN 0-13-805326-X. Note that the law relating flux to EMF, which this article calls "Faraday's law", is referred to by Griffiths as the "universal flux rule". He uses the term "Faraday's law" to refer to what this article calls the "Maxwell–Faraday equation".
  23. ^ "The flux rule" is the terminology that Feynman uses to refer to the law relating magnetic flux to EMF. Feynman, R. P.; Leighton, R. B.; Sands, M. L. (2006). The Feynman Lectures on Physics, Volume II. Pearson/Addison-Wesley. p. 17-2. ISBN 0-8053-9049-9.
  24. ^ Einstein, A. (1905). "Zur Elektrodynamik bewegter Körper". Annalen der Physik. 17 (10): 891–921. Bibcode:1905AnP...322..891E. doi:10.1002/andp.19053221004.
    Translated in Einstein, A. (1923). "On the Electrodynamics of Moving Bodies" (PDF). The Principle of Relativity. Jeffery, G.B.; Perret, W. (transl.). London: Methuen and Company.
  25. ^ a b c Images and reference text are from the public domain book: Hawkins Electrical Guide, Volume 1, Chapter 19: Theory of the Armature, pp. 270–273, Copyright 1917 by Theo. Audel & Co., Printed in the United States

Further reading

External links

Electromotive force

Electromotive force, abbreviated emf (denoted and measured in volts), is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator. A device that converts other forms of energy into electrical energy (a "transducer") provides an emf as its output. (The word "force" in this case is not used to mean mechanical force, as may be measured in pounds or newtons.)

In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop. For a time-varying magnetic flux linking a loop, the electric potential scalar field is not defined due to a circulating electric vector field, but an emf nevertheless does work that can be measured as a virtual electric potential around the loop. (While electrical charges travel around the loop, their energy is typically converted into thermal energy due to the resistance of the conductor comprising the loop.)

In the case of a two-terminal device (such as an electrochemical cell) which is modeled as a Thévenin's equivalent circuit, the equivalent emf can be measured as the open-circuit potential difference or "voltage" between the two terminals. This potential difference can drive an electric current if an external circuit is attached to the terminals.

Faraday's law of induction

Faraday's law of induction (shortly called Faraday's law throughout this document) 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.The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.

Historically, Faraday's law had been discovered and one aspect of it (transformer EMF) was formulated as the Maxwell–Faraday equation later. Interestingly, the equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer EMF) and the Lorentz force (describing motional EMF). The integral form of the Maxwell–Faraday equation describes only the transformer EMF, while the equation of Faraday's law describes both the transformer EMF and the motional EMF.

Giuseppe Domenico Botto

Giuseppe Domenico Botto (4 April 1791 – 20 March 1865) was an Italian physicist.

Born at Moneglia, he studied at the University of Genoa and the École Polytechnique in Paris. The chair of General and Experimental Physics was assigned to G.D Botto in 1828. Experimental work was dedicated to magnetic, thermal, and chemical effects of electrical currents and induction of currents.In 1830 Botto described in a note a prototype electric motor on which he was working and published a description of it in a Memoria titled "Machine Loco-motive mise en mouvement par l'électro-magnétisme" to the Academy of Turin around 1836.

A device built on the basis of his description was part of the collection of scientific instruments of the Grand Duke of Tuscany, which is now kept at the Institute and Museum of History of Science in Florence. In the following years he published more work on improving efficiency of electric motors.

Botto experimented with electrolysis of water using a manual generator of electric sparks, the electric magnet designed by Leopoldo Nobili and Vincenzo Antinori on the basis of the discovery of' electromagnetic induction made by Michael Faraday in 1831. In 1833 he tested an iron-platinum thermocouple wrapped as a chain around a wooden stick which generated a current when heat from a flame was applied,. The heat from the flame created a temperature difference, and the thermocouple converted the temperature difference into an electric voltage.He also worked on other subjects and published in 1846 a note for the improvement of agriculture in Piedmont. In 1849 he proposed a new system for transmission and encoding for the electrical telegraph system (notes on this subject were recently discovered in the archives of the Museo Sanguineti Leonardini of Chiavari.)

He died at Turin in 1865.

Henry (unit)

The henry (symbol: H) is the SI derived unit of electrical inductance. If a current of 1 ampere flowing through the coil produces flux linkage of 1 weber turn, the coil has a self inductance of 1 henry.‌ The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.

Hippolyte Pixii

Hippolyte Pixii (1808–1835) was an instrument maker from Paris, France. In 1832 he built an early form of alternating current electrical generator, based on the principle of electromagnetic induction discovered by Michael Faraday. Pixii's device was a spinning magnet, operated by a hand crank, where the north and south poles passed over a coil with an iron core. A current pulse was produced each time a pole passed over the coil. He also found that the current direction changed when the north pole passed over the coil after the south pole. Later, acting on a suggestion by André-Marie Ampère, other results were obtained by introducing a commutator which produced a pulsating direct current. At that time direct current was preferable to alternating current. Although Pixii did not fully understand electromagnetic induction, his device led to more sophisticated devices being constructed.

IET Faraday Medal

The Faraday Medal is the top medal awarded by the Institution of Engineering and Technology (IET) (previously called the Institution of Electrical Engineers). It is part of the IET Achievement Medals collection of awards. The medal is named after the famous Michael Faraday FRS, the father of electromagnetism. Faraday is widely recognized as a top scientist, engineer, chemist, and inventor. His electromagnetic induction principles have been widely used in electric motors and generators today.

Inductive coupling

In electrical engineering, two conductors are said to be inductively coupled or magnetically coupled when they are configured such that a change in current through one wire induces a voltage across the ends of the other wire through electromagnetic induction. A changing current through the first wire creates a changing magnetic field around it by Ampere's circuital law. The changing magnetic field induces an electromotive force (EMF or voltage) in the second wire by Faraday's law of induction. The amount of inductive coupling between two conductors is measured by their mutual inductance.

The coupling between two wires can be increased by winding them into coils and placing them close together on a common axis, so the magnetic field of one coil passes through the other coil. Coupling can also be increased by a magnetic core of a ferromagnetic material like iron or ferrite in the coils, which increases the magnetic flux. The two coils may be physically contained in a single unit, as in the primary and secondary windings of a transformer, or may be separated. Coupling may be intentional or unintentional. Unintentional inductive coupling can cause signals from one circuit to be induced into a nearby circuit, this is called cross-talk, and is a form of electromagnetic interference.

An inductively coupled transponder consists of a solid state transceiver chip connected to a large coil that functions as an antenna. When brought within the oscillating magnetic field of a reader unit, the transceiver is powered up by energy inductively coupled into its antenna and transfers data back to the reader unit inductively.

Magnetic coupling between two magnets can also be used to mechanically transfer power without contact, as in the magnetic gear.

Inductive sensor

An inductive sensor is a device that uses the principle of electromagnetic induction to detect or measure objects. An inductor develops a magnetic field when a current flows through it; alternatively, a current will flow through a circuit containing an inductor when the magnetic field through it changes. This effect can be used to detect metallic objects that interact with a magnetic field. Non-metallic substances such as liquids or some kinds of dirt do not interact with the magnetic field, so an inductive sensor can operate in wet or dirty conditions.

Inductively coupled plasma

An inductively coupled plasma (ICP) or transformer coupled plasma (TCP) is a type of plasma source in which the energy is supplied by electric currents which are produced by electromagnetic induction, that is, by time-varying magnetic fields.

Jefimenko's equations

In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects. Therefore they can be used for moving charges and currents. They are the general solutions to Maxwell's equations for any arbitrary distribution of charges and currents.

Lenz's law

Lenz's law (pronounced /ˈlɛnts/), named after the physicist Emil Lenz who formulated it in 1834, 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. Or as informally, yet concisely summarised by D.J. Griffiths:

Lenz's law is shown by the negative sign in Faraday's law of induction:

which indicates that the induced electromotive force and the rate of change in magnetic flux have opposite signs. It is a qualitative law that specifies the direction of induced current but says 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 why eddy currents exert a drag force on moving objects in a magnetic field.

Lenz's law can be seen as analogous to Newton's third law in classic mechanics.

For a rigorous mathematical treatment, see electromagnetic induction and Maxwell's equations.

Linear alternator

A linear alternator is essentially a linear motor used as an electrical generator.

An alternator is a type of alternating current (AC) electrical generator. The devices are often physically equivalent. The principal difference is in how they are used and which direction the energy flows. An alternator converts mechanical energy to electrical energy, whereas a motor converts electrical energy to mechanical energy. Like most electric motors and electric generators, the linear alternator works by the principle of electromagnetic induction. However, most alternators work with rotary motion, whereas "linear" alternators work with "linear" motion (i.e. motion in a straight line).

Magnetic flow meter

A magnetic flow meter (mag meter, electromagnetic flow meter) is a transducer that measures fluid flow by the voltage induced across the liquid by its flow through a magnetic field. A magnetic field is applied to the metering tube, which results in a potential difference proportional to the flow velocity perpendicular to the flux lines. The physical principle at work is electromagnetic induction. The magnetic flow meter requires a conducting fluid, for example, water that contains ions, and an electrical insulating pipe surface, for example, a rubber-lined steel tube.

If the magnetic field direction were constant, electrochemical and other effects at the electrodes would make the potential difference

difficult to distinguish from the fluid flow induced potential difference. To mitigate this in modern magnetic flowmeters, the magnetic field is constantly reversed, cancelling out the electrochemical potential difference, which does not change direction with the magnetic field. This however prevents the use of permanent magnets for magnetic flowmeters.

Online Electric Vehicle

The Online Electric Vehicle (OLEV) is an electric vehicle that charges wirelessly while moving using electromagnetic induction (the wireless transfer of power through magnetic fields). It functions by using a segmented "recharging" road that induces a current in "pick-up" modules on the vehicle.

OLEV is the first public transport system that used a "recharging" road and was first launched on March 9, 2010 by The Korea Advanced Institute of Science and Technology (KAIST).

Radio-frequency induction

For the common use of RF induction process of heating a metal object by electromagnetic induction, see induction heatingRadio-frequency induction or RF induction is the use of a radio frequency magnetic field to transfer energy by means of electromagnetic induction in the near field. A radio-frequency alternating current is passed through a coil of wire that acts as the transmitter, and a second coil or conducting object, magnetically coupled to the first coil, acts as the receiver.

Related rates

In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Differentiation with respect to time or one of the other variables requires application of the chain rule, since most problems involve several variables.

Fundamentally, if a function is defined such that , then the derivative of the function can be taken with respect to another variable. (The Variable is frequently used as many Related Rates problems apply to finding changes with respect to time.) We assume is a function of , i.e. . Then , so

Written in Leibniz notation, this is:

The value of this is: if it is known how changes with respect to , then we can determine how changes with respect to and vice versa. We can extend this application of the chain rule with the sum, difference, product and quotient rules of calculus, etc.



then .

Vacuum induction melting

Vacuum induction melting (VIM) utilizes electric currents to melt metal within a vacuum. The first prototype was developed in 1920. One of the only ways to induce a current within a conductor is through electromagnetic induction. Electromagnetic induction induces eddy currents within conductors by changing the magnetic field. Eddy currents create heating effects to melt the metal. Vacuum induction melting has been used in both the aerospace and nuclear industries.


Wireless communication, or sometimes simply wireless, is the transfer of information or power between two or more points that are not connected by an electrical conductor. The most common wireless technologies use radio waves. With radio waves distances can be short, such as a few meters for Bluetooth or as far as millions of kilometers for deep-space radio communications. It encompasses various types of fixed, mobile, and portable applications, including two-way radios, cellular telephones, personal digital assistants (PDAs), and wireless networking. Other examples of applications of radio wireless technology include GPS units, garage door openers, wireless computer mice, keyboards and headsets, headphones, radio receivers, satellite television, broadcast television and cordless telephones. Somewhat less common methods of achieving wireless communications include the use of other electromagnetic wireless technologies, such as light, magnetic, or electric fields or the use of sound.

The term wireless has been used twice in communications history, with slightly different meaning. It was initially used from about 1890 for the first radio transmitting and receiving technology, as in wireless telegraphy, until the new word radio replaced it around 1920. The term was revived in the 1980s and 1990s mainly to distinguish digital devices that communicate without wires, such as the examples listed in the previous paragraph, from those that require wires or cables. This became its primary usage in the 2000s, due to the advent of technologies such as mobile broadband, Wi-Fi and Bluetooth.

Wireless operations permit services, such as long-range communications, that are impossible or impractical to implement with the use of wires. The term is commonly used in the telecommunications industry to refer to telecommunications systems (e.g. radio transmitters and receivers, remote controls, etc.) which use some form of energy (e.g. radio waves, acoustic energy,) to transfer information without the use of wires. Information is transferred in this manner over both short and long distances.

Wireless telegraphy

Wireless telegraphy means transmission of telegraph signals by radio waves; a more specific term for this is radiotelegraphy. Before about 1910 when radio became dominant, the term wireless telegraphy was also used for various other experimental technologies for transmitting telegraph signals without wires, such as electromagnetic induction, and ground conduction telegraph systems.Radiotelegraphy was the first means of radio communication; the first practical radio transmitters and receivers invented in 1894-5 by Guglielmo Marconi used radiotelegraphy. It continued to be the only type of radio transmission during the first three decades of radio, called the "wireless telegraphy era" up until World War I, when the development of amplitude modulation (AM) radiotelephony allowed sound (audio) to be transmitted by radio. In radiotelegraphy, information is transmitted by pulses of radio waves of two different lengths called "dots" and "dashes", which spell out text messages, usually in Morse code. In a manual system, the sending operator taps on a switch called a telegraph key which turns the transmitter on and off, producing the pulses of radio waves. At the receiver the pulses are audible in the receiver's speaker as beeps, which are translated back to text by an operator who knows Morse code.

Radiotelegraphy was used for long distance person-to-person commercial, diplomatic, and military text communication throughout the first half of the 20th century. It became a strategically important capability during the two world wars, since a nation without long distance radiotelegraph stations could be isolated from the rest of the world by an enemy cutting its submarine telegraph cables. Beginning about 1908, powerful transoceanic radiotelegraphy stations transmitted commercial telegram traffic between countries at rates up to 200 words per minute. Radiotelegraphy was transmitted by several different modulation methods during its history. The primitive spark gap transmitters used until 1920 transmitted damped waves, which had very large bandwidth and tended to interfere with other transmissions. This type of emission was banned by 1930. The vacuum tube (valve) transmitters which came into use after 1920 transmitted code by pulses of unmodulated sinusoidal carrier wave called continuous waves (CW), which is still used today. To make CW transmissions audible, the receiver requires a circuit called a beat frequency oscillator (BFO). A third type of modulation, frequency shift keying (FSK) was used mainly by radioteletypes. Morse code radiotelegraphy was gradually replaced by radioteletype networks (RTTY) in most high volume applications by World War 2. Today it is nearly obsolete, the only remaining users are the radio amateur community and some limited training by the military for emergency use.

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