= Electromagnetism
{wiki}
Electromagnetism describes how <electric charge> and <electric current> interact through the <electric field> $\mathbf E$ and <magnetic field> $\mathbf B$. The <Maxwell equations> describe the fields and their sources; the <Lorentz force> describes the response of a particle of <electric charge> $q$ and <velocity> $\mathbf v$:
$$
\mathbf F=q(\mathbf E+\mathbf v\times\mathbf B),\qquad
\frac{d\mathcal E_{\mathrm{particle}}}{dt}=q\mathbf E\cdot\mathbf v.
$$
The <electric field> can change the particle's <energy>. The magnetic part of the <Lorentz force> is perpendicular to <velocity>, so <magnetic forces do no work>; they can bend a trajectory. These are local interactions: a particle responds to the <electromagnetic field> at its position. https://www.feynmanlectures.caltech.edu/II_01.html[Feynman lectures, II.1: fields and forces]{ref}.
The remarkable unification is that the same <Maxwell equations> connect <Coulomb's law>, <Faraday's law of induction>, and freely propagating <electromagnetic waves>. A changing <electric field> contributes to magnetic circulation through <displacement current>; together with <Faraday's law>, this permits waves in vacuum without conducting matter. The <Poynting theorem> then explains how the fields store and transport <energy>. This connects the force on a charge to the energy carried by light.
In his 1865 paper, <James Clerk Maxwell> derived transverse disturbances and compared the propagation speed inferred from electrical measurements with independently measured light speeds. Part VI, especially §§95–97, argues that their agreement supports identifying light as an <electromagnetic wave>. This was a comparison with finite experimental accuracy, rather than a numerical identity between the historical measurements. https://royalsocietypublishing.org/doi/10.1098/rstl.1865.0008[Maxwell, A Dynamical Theory of the Electromagnetic Field, Philosophical Transactions 155 (1865), 459–512]{ref}; https://en.wikisource.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field/Part_VI[transcription of Maxwell's original Part VI]{ref}.
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