View source for Magnetomotive force

{{Short description|Concept in physics}}
{{Electromagnetism|Magnetic circuit}}

In [[physics]], the '''magnetomotive force''' (abbreviated '''mmf''' or '''MMF''', symbol <math>\mathcal F</math>) is a quantity appearing in the equation for the [[magnetic flux]] in a [[magnetic circuit]], Hopkinson's law.<ref>Waygood, p. 137</ref> It is the property of certain substances or phenomena that give rise to [[magnetic fields]]:
<math display="block"> \mathcal{F} = \Phi \mathcal{R} ,</math>
where {{math|Φ}} is the magnetic flux and <math>\mathcal{R}</math> is the [[reluctance]] of the circuit.  It can be seen that the magnetomotive force plays a role in this equation analogous to the voltage {{mvar|V}} in [[Ohm's law]], {{math|1=''V'' = ''IR''}}, since it is the cause of magnetic flux in a magnetic circuit:<ref>Smith, pp. 495–506</ref>
# <math>\mathcal{F} = NI</math> {{pb}} where {{mvar|N}} is the number of turns in a [[inductor|coil]] and {{mvar|I}} is the [[electric current]] through the coil.
# <math>\mathcal{F} = \Phi \mathcal{R}</math> {{pb}} where {{math|Φ}} is the [[magnetic flux]] and <math>\mathcal{R}</math> is the [[magnetic reluctance]]
# <math>\mathcal{F} = HL</math> {{pb}} where {{math|''H''}} is the magnetizing force (the strength of the [[Magnetic field#The H-field|magnetizing field]]) and {{mvar|L}} is the mean length of a [[solenoid]] or the circumference of a [[toroid]].

==Units==
The [[International System of Units|SI unit]] of mmf is the [[ampere]], the same as the unit of current{{sfn|Newell|Tiesinga|2019|p=19}} (analogously the units of [[Electromotive force|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 (unit)|gilbert]] may also be encountered.

==History==
The term ''magnetomotive force'' was coined by [[Henry Augustus Rowland]] in 1880.  Rowland intended this to indicate a direct analogy with [[electromotive force]].<ref>{{multiref|Hon & Goldstein, pp. 638–639|Rowland (1880), pp. 92, 97}}</ref>  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.<ref>{{multiref|Thompson, p. viii|Rowland (1873), p. 143}}</ref>

''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.<ref>{{multiref|See for instance|Schmidt & Schitter, p. 340, or|Waygood, p. 137}}</ref>  According to a review of magnetic circuit analysis methods this is an incorrect attribution originating from an 1885 paper by Hopkinson.<ref>Lambert ''et al.'', p. 2427</ref>  Furthermore, Hopkinson actually cites Rowland's 1873 paper in this work.<ref>Hopkinson, p. 455</ref>

==References==
{{reflist|23em}}

==Bibliography==
===Cited sources===

* Hon, Giora; Goldstein, Bernard R, [https://www.sciencedirect.com/science/article/pii/S1355219806000487 "Symmetry and asymmetry in electrodynamics from Rowland to Einstein"], ''Studies in History and Philosophy of Modern Physics'', vol. 37, iss. 4, pp.&nbsp;635–660, Elsevier December 2006.
* Hopkinson, John, [http://rstl.royalsocietypublishing.org/content/176/455 "Magnetisation of iron"], ''Philosophical Transactions of the Royal Society'', vol. 176, pp.&nbsp;455–469, 1885.
* Lambert, Mathieu; Mahseredjian, Jean; Martínez-Duró, Manuel; Sirois, Frédéric, [https://ieeexplore.ieee.org/abstract/document/7008520/ "Magnetic circuits within electric circuits: critical review of existing methods and new mutator implementations"], ''IEEE Transactions on Power Delivery'', vol. 30, iss. 6, pp.&nbsp;2427–2434, December 2015.
* {{cite report |editor1-last= Newell |editor1-first= David B. |editor2-last= Tiesinga |editor2-first= Eite |date= 2019 |title= NIST Special Publication 330: The International System of Units (SI) |edition= 2019 |publisher= [[National Institute of Standards and Technology]] |doi= 10.6028/NIST.SP.330-2019 |type= Standards publication|doi-access= free }}
* Rowland, Henry A, [https://archive.org/stream/s4philosophicalm46lond#page/140/mode/2up/ "On magnetic permeability and the maximum magnetism of iron, steel, and nickel"], ''Philosophical Magazine'', series 4, vol. 46, no. 304, pp.&nbsp;140–159, August 1873.
* Rowland, Henry A, [https://www.jstor.org/stable/2369444 "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"] ([https://www.jstor.org/stable/2369465 part 2]), ''American Journal of Mathematics'', vol. 3, nos. 1–2, pp.&nbsp;89–113, March 1880.
* Schmidt, Robert Munnig; Schitter, Georg, [https://books.google.com/books?id=3WvnAgAAQBAJ&pg=PA340 "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}}.
* [[Silvanus P. Thompson|Thompson, Silvanus Phillips]], [https://books.google.com/books?id=x6G7rPCcPfgC&pg=PR8 ''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, [https://books.google.com/books?id=8qHGRTC7h-MC&pg=PT157 ''An Introduction to Electrical Science''], Routledge, 2013 {{ISBN|1135071136}}.

===General references===
* ''The Penguin Dictionary of Physics'', 1977, {{ISBN|0-14-051071-0}}
* ''A Textbook of Electrical Technology'', 2008, {{ISBN|81-219-2440-5}}

[[Category:Magnetism]]
[[Category:Physical quantities]]

[[it:Forza magnetomotrice]]