Editing Lorentz force (section)

== Electromotive force ==
{{main|Electromotive force}}
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| image1            = Elementary generator.svg
| caption1          = Motional EMF, induced by moving a conductor through a magnetic field.
| image2            = Alternator 1.svg
| caption2          = Transformer EMF, induced by a changing magnetic field.
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}}

The magnetic force ({{math|''q'''''v''' × '''B'''}}) component of the Lorentz force is responsible for [[Electromotive_force#Electromagnetic_induction|motional electromotive force]] (or ''motional EMF''), the phenomenon underlying many electrical generators. When a conductor is moved through a magnetic field, the magnetic field exerts opposite forces on electrons and nuclei in the wire, and this creates the EMF. The term "motional EMF" is applied to this phenomenon, since the EMF is due to the ''motion'' of the wire.{{sfn|Griffiths|2023|p=307}}

In other electrical generators, the magnets move, while the conductors do not. In this case, the EMF is due to the electric force ({{math|''q'''''E'''}}) term in the Lorentz Force equation. The electric field in question is created by the changing magnetic field, resulting in an induced EMF called the ''transformer EMF'', as described by the [[Electromagnetic induction#Maxwell–Faraday equation|Maxwell–Faraday equation]] (one of the four modern [[Maxwell's equations]]).{{sfn|Sadiku|2018|pp=424-427}}

Both of these EMFs, despite their apparently distinct origins, are described by the same equation, namely, the EMF is the rate of change of [[magnetic flux]] through the wire. (This is Faraday's law of induction, see [[Lorentz force#Lorentz force and Faraday.27s law of induction|below]].) Einstein's [[special theory of relativity]] was partially motivated by the desire to better understand this link between the two effects.{{sfn|Griffiths|2023|pp=316-318}} In fact, the electric and magnetic fields are different facets of the same electromagnetic field, and in moving from one inertial frame to another, the [[solenoidal vector field]] portion of the {{math|'''E'''}}-field can change in whole or in part to a {{math|'''B'''}}-field or ''vice versa''.<ref name=Chow>{{cite book | author=Tai L. Chow | title=Electromagnetic theory | year= 2006 | page = 395 | publisher = Jones and Bartlett | location=Sudbury, Massachusetts | isbn=0-7637-3827-1 | url=https://books.google.com/books?id=dpnpMhw1zo8C&pg=PA153 }}</ref>