Magnetomotive force

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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 Study of the fundamental properties of matter and energy

Physics is the natural science that studies matter and 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.

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 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]

Ohms law law about electricity

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:

  1. = NI
    where N is the number of turns in the coil and I is the electric current through the circuit.
  2. = ΦR
    where Φ is the magnetic flux and R is the magnetic reluctance
  3. = 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


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.

International System of Units a system of units of measurement for base and derived physical quantities

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 ampere, kelvin, second, metre, kilogram, candela, mole, 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.

Ampere SI base unit of electric current

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 scalar physical quantity

Electromotive force, abbreviated emf, 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 provides an emf as its output.


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]

Henry Augustus Rowland American physicist

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 English scientist

Michael Faraday FRS was a British 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 Scottish physicist

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.

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  1. Waygood, p. 137
  2. Smith, pp. 495-506
  3. Hon & Goldstein, pp. 638-639
    • Rowland (1880), pp. 92, 97
  4. Thompson, p. viii
    • Rowland (1873), p. 143
  5. See for instance
    • Schmidt & Schitter, p. 340, or
    • Waygood, p. 137
  6. Lambert et al., p. 2427
  7. Hopkinson, p. 455


Cited sources

International Standard Book Number Unique numeric book identifier

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Silvanus P. Thompson British academic physicist

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.

General references