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The third of Maxwell's equations is called the [[Ampere-maxwell law|Ampère–Maxwell law]]. It states that a magnetic field can be generated by an [[electric current]].<ref>{{Cite web|title=Ampere's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref> The direction of the magnetic field is given by Ampère's [[right-hand grip rule]]. If the wire is straight, then the magnetic field is curled around it like the gripped fingers in the right-hand rule. If the wire is wrapped into coils, then the magnetic field inside the coils points in a straight line like the outstretched thumb in the right-hand grip rule.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)| isbn=0-471-92711-2|edition=2nd| series=The Manchester Physics Series| ___location=Chichester [England]| pages=125|oclc=21447877}}</ref> When electric currents are used to produce a [[magnet]] in this way, it is called an [[electromagnet]]. Electromagnets often use a wire curled up into [[solenoid]] around an iron core which strengthens the magnetic field produced because the iron core becomes magnetised.<ref name=":8">{{Cite web |title=Magnets and Electromagnets |url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c1 |access-date=2020-11-27| website=hyperphysics.phy-astr.gsu.edu}}</ref><ref name=":9">{{Cite web|title=Ferromagnetism|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c4 |access-date=2020-11-27 |website=hyperphysics.phy-astr.gsu.edu}}</ref> Maxwell's extension to the law states that a time-varying electric field can also generate a magnetic field.<ref name=":5" /> Similarly, [[Faraday's law of induction]] states that a magnetic field can produce an electric current. For example, a magnet pushed in and out of a coil of wires can produce an electric current in the coils which is proportional to the strength of the magnet as well as the number of coils and the speed at which the magnet is inserted and extracted from the coils. This principle is essential for [[transformer]]s which are used to transform currents from high [[voltage]] to low voltage, and vice versa. They are needed to convert high voltage [[mains electricity]] into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the [[Maxwell–Faraday equation]]—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field.
[[File:EM Spectrum Properties (Amplitude Corrected).svg|thumb|440x440px|The [[electromagnetic spectrum]]]]
Together, Maxwell's equations provide a single uniform theory of the electric and magnetic fields and Maxwell's work in creating this theory has been called "the second great unification in physics" after the first great unification of [[Newton's law of universal gravitation]].<ref>{{Cite journal|last=Editors|first=AccessScience|date=2014|title=Unification theories and a theory of everything| url=https://www.accessscience.com/content/unification-theories-and-a-theory-of-everything/BR0814141|journal=Access Science| language=en|doi=10.1036/1097-8542.BR0814141}}</ref> The solution to Maxwell's equations in [[free space]] (where there are no charges or currents) produces [[wave equation]]s corresponding to [[electromagnetic waves]] (with both electric and magnetic components) travelling at the [[speed of light]].<ref>{{Cite book| last=Grant | first = Ian S. | url=https://www.worldcat.org/oclc/21447877| title=Electromagnetism|date=1990 |publisher=Wiley | others=Phillips, W. R. (William Robert) | isbn=0-471-92711-2 | edition=2nd|series=The Manchester Physics Series| ___location=Chichester [England]| pages=365 |oclc=21447877}}</ref> The observation that these wave solutions had a wave speed exactly equal to the speed of light led Maxwell to hypothesise that light is a form of electromagnetic radiation and to posit that other electromagnetic radiation could exist with different wavelengths.<ref name="ADTEF">{{cite journal | last=Maxwell|first=James Clerk| year=1865 |title=A dynamical theory of the electromagnetic field | url=http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf| url-status=live |journal=Philosophical Transactions of the Royal Society of London |volume=155 |pages=459–512 |bibcode=1865RSPT..155..
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