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In physics, the **magnetomotive force** (mmf) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, often called Ohm's law for magnetic circuits.^{ [1] } It is the property of certain substances or phenomena that give rise to magnetic fields:

**Physics** is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

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.

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.

where *Φ* is the magnetic flux and *R* is the reluctance of the circuit. It can be seen that the magnetomotive force plays a role in this equation analogous to the voltage *V* in Ohm's law: *V* = *IR,* since it is the cause of magnetic flux in a magnetic circuit:^{ [2] }

**Ohm's law** states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

*ℱ*=*NI*- where
*N*is the number of turns in the coil and*I*is the electric current through the circuit.

- where
*ℱ*=*ΦR*- where
*Φ*is the magnetic flux and*R*is the magnetic reluctance

- where
*ℱ*=*HL*- where
*H*is the magnetizing force (the strength of the magnetizing field) and*L*is the mean length of a solenoid or the circumference of a toroid.

- where

The SI unit of mmf is the ampere, the same as the unit of current (analogously the units of emf and voltage are both the volt). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the MKS system. Occasionally, the cgs system unit of the gilbert may also be encountered.

The **International System of Units** is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the second, metre, kilogram, ampere, kelvin, mole, candela, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

The **ampere**, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

**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.

The term *magnetomotive force* was coined by Henry Augustus Rowland in 1880. Rowland intended this to indicate a direct analogy with electromotive force.^{ [3] } The idea of a magnetic analogy to electromotive force can be found much earlier in the work of Michael Faraday (1791-1867) and it is hinted at by James Clerk Maxwell (1831-1879). However, Rowland coined the term and was the first to make explicit an Ohm's law for magnetic circuits in 1873.^{ [4] }

Prof **Henry Augustus Rowland** FRS(For) HFRSE was an American physicist. Between 1899 and 1901 he served as the first president of the American Physical Society. He is remembered today particularly for the high quality of the diffraction gratings he made and for the work he did with them on the solar spectrum.

**Michael Faraday** FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism and electrolysis.

**James Clerk Maxwell** was a Scottish scientist in the field of mathematical physics. His most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the "second great unification in physics" after the first one realised by Isaac Newton.

*Ohm's law for magnetic circuits* is sometimes referred to as Hopkinson's law rather than Rowland's law as some authors attribute the law to John Hopkinson instead of Rowland.^{ [5] } According to a review of magnetic circuit analysis methods this is an incorrect attribution originating from an 1885 paper by Hopkinson.^{ [6] } Furthermore, Hopkinson actually cites Rowland's 1873 paper in this work.^{ [7] }

**John Hopkinson,** FRS, was a British physicist, electrical engineer, Fellow of the Royal Society and President of the IEE twice in 1890 and 1896. He invented the three-wire (three-phase) system for the distribution of electrical power, for which he was granted a patent in 1882. He also worked in many areas of electromagnetism and electrostatics, and in 1890 was appointed professor of electrical engineering at King's College London, where he was also director of the Siemens Laboratory.

In physics the **Lorentz force** is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge *q* moving with a velocity **v** in an electric field **E** and a magnetic field **B** experiences a force of

The **volt** is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

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.

The **oersted** is the unit of the auxiliary magnetic field **H** in the centimetre–gram–second system of units (CGS). It is equivalent to 1 dyne per maxwell.

**Electromagnetic** or **magnetic induction** is the production of an electromotive force across an electrical conductor in a changing magnetic field.

An **electromagnet** is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole, denoting the center of the coil. The magnetic field disappears when the current is turned off. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.

The **ampere-turn** (At) is the MKS unit of magnetomotive force (MMF), represented by a direct current of one ampere flowing in a single-turn loop in a vacuum. "Turns" refers to the winding number of an electrical conductor composing an inductor.

In classical electromagnetism, **Ampère's circuital law** relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 paper "On Physical Lines of Force" and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.

In electromagnetism, **displacement current density** is the quantity ∂* D*/∂

"**A Dynamical Theory of the Electromagnetic Field**" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and deduces that light is an electromagnetic wave.

**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.

**Permeance**, in general, is the degree to which a material admits a flow of matter or energy. Permeance is usually represented by a curly capital P: .

The **Faraday paradox** or **Faraday's paradox** is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes:

**Magnetic reluctance**, or **magnetic resistance**, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry and composition of an object.

**Magnetic complex reluctance** is a measurement of a passive magnetic circuit dependent on sinusoidal magnetomotive force and sinusoidal magnetic flux, and this is determined by deriving the ratio of their complex *effective* amplitudes.[Ref. 1-3]

Magnets exert forces and torques on each other due to the rules of electromagnetism. The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary **force between magnets**, therefore, is the magnetic dipole–dipole interaction. If all of the magnetic dipoles that make up two magnets are known then the net force on both magnets can be determined by summing up all these interactions between the dipoles of the first magnet and that of the second.

An **electropermanent magnet** or **EPM** is a type of permanent magnet in which the external magnetic field can be switched on or off by a pulse of electric current in a wire winding around part of the magnet. The magnet consists of two sections, one of "hard" magnetic material and one of "soft" material. The direction of magnetization in the latter piece can be switched by a pulse of current in a wire winding about the former. When the magnetically soft and hard materials have opposing magnetizations, the magnet produces no net external field across its poles, while when their direction of magnetization is aligned the magnet produces an external magnetic field.

- Hon, Giora; Goldstein, Bernard R, "Symmetry and asymmetry in electrodynamics from Rowland to Einstein",
*Studies in History and Philosophy of Modern Physics*, vol. 37, iss. 4, pp. 635-660, Elsevier December 2006. - Hopkinson, John, "Magnetisation of iron",
*Philosophical Transactions of the Royal Society*, vol. 176, pp. 455-469, 1885. - Lambert, Mathieu; Mahseredjian, Jean; Martínez-Duró, Manuel; Sirois, Frédéric, "Magnetic circuits within electric circuits: critical review of existing methods and new mutator implementations",
*IEEE Transactions on Power Delivery*, vol. 30, iss. 6, pp. 2427-2434, December 2015. - Rowland, Henry A, "On magnetic permeability and the maximum magnetism of iron, steel, and nickel",
*Philosophical Magazine*, series 4, vol. 46, no. 304, pp. 140-159, August 1873. - Rowland, Henry A, "On the general equations of electro-magnetic action, with application to a new theory of magnetic attractions, and to the theory of the magnetic rotation of the plane of polarization of light" (part 2),
*American Journal of Mathematics*, vol. 3, nos. 1-2, pp. 89–113, March 1880. - Schmidt, Robert Munnig; Schitter, Georg, "Electromechanical actuators", ch. 5 in Schmidt, Robert Munnig; Schitter, Georg; Rankers, Adrian; van Eijk, Jan,
*The Design of High Performance Mechatronics*, IOS Press, 2014 ISBN 1614993688. - Thompson, Silvanus Phillips,
*The Electromagnet and Electromagnetic Mechanism*, Cambridge University Press, 2011 (first published 1891) ISBN 1108029213. - Smith, R.J. (1966),
*Circuits, Devices and Systems*, Chapter 15, Wiley International Edition, New York. Library of Congress Catalog Card No. 66-17612 - Waygood, Adrian,
*An Introduction to Electrical Science*, Routledge, 2013 ISBN 1135071136.

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

**Silvanus Phillips Thompson** was a professor of physics at the City and Guilds Technical College in Finsbury, England. He was elected to the Royal Society in 1891 and was known for his work as an electrical engineer and as an author. Thompson's most enduring publication is his 1910 text *Calculus Made Easy*, which teaches the fundamentals of infinitesimal calculus, and is still in print. Thompson also wrote a popular physics text, *Elementary Lessons in Electricity and Magnetism,* as well as biographies of Lord Kelvin and Michael Faraday.

*The Penguin Dictionary of Physics*, 1977, ISBN 0-14-051071-0*A Textbook of Electrical Technology*, 2008, ISBN 81-219-2440-5

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