Editing Maxwell's equations (section)

=== Ampère–Maxwell law ===
{{Main|Ampère's circuital law}}
[[Image:Magnetic core.jpg|right|thumb|[[Magnetic-core memory]] (1954) is an application of [[Ampère's circuital law]]. Each [[magnetic core|core]] stores one [[bit]] of data.]]

The original law of Ampère states that magnetic fields relate to [[electric current]]. [[Ampère–Maxwell law|Maxwell's addition]] states that magnetic fields also relate to changing electric fields, which Maxwell called [[displacement current]]. The integral form states that electric and displacement currents are associated with a proportional magnetic field along any enclosing curve.

Maxwell's modification of Ampère's circuital law is important because the laws of Ampère and Gauss must otherwise be adjusted for static fields.<ref>J. D. Jackson, ''Classical Electrodynamics'', section 6.3</ref>{{clarify|date=May 2022}} As a consequence, it predicts that a rotating magnetic field occurs with a changing electric field.<ref name="VideoGlossary" /><ref>[https://books.google.com/books?id=1DZz341Pp50C&pg=PA809 ''Principles of physics: a calculus-based text''], by R. A. Serway, J. W. Jewett, page 809.</ref> A further consequence is the existence of self-sustaining [[electromagnetic waves]] which [[electromagnetic wave equation|travel through empty space]].

The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents,<ref group="note">The quantity we would now call {{math|(''ε''{{sub|0}}''μ''{{sub|0}})<sup>−1/2</sup>}}, with units of velocity, was directly measured before Maxwell's equations, in an 1855 experiment by [[Wilhelm Eduard Weber]] and [[Rudolf Kohlrausch]]. They charged a [[leyden jar]] (a kind of [[capacitor]]), and measured the [[Coulomb's law|electrostatic force]] associated with the potential; then, they discharged it while measuring the [[Ampère's force law|magnetic force]] from the current in the discharge wire. Their result was {{val|3.107|e=8|ul=m/s}}, remarkably close to the speed of light. See Joseph F. Keithley, [https://books.google.com/books?id=uwgNAtqSHuQC&pg=PA115 ''The story of electrical and magnetic measurements: from 500&nbsp;B.C. to the 1940s'', p.&nbsp;115].</ref> matches the [[speed of light]]; indeed, [[light]] ''is'' one form of [[electromagnetic radiation]] (as are [[X-ray]]s, [[radio wave]]s, and others). Maxwell understood the connection between electromagnetic waves and light in 1861, thereby unifying the theories of [[electromagnetism]] and [[optics]].