Editing Force (section)

=== Electromagnetic ===
{{main|Electromagnetic force}}
The [[electrostatic force]] was first described in 1784 by Coulomb as a force that existed intrinsically between two [[electric charge|charges]].<ref name=Cutnell/>{{rp|519}} The properties of the electrostatic force were that it varied as an [[inverse square law]] directed in the [[polar coordinates|radial direction]], was both attractive and repulsive (there was intrinsic [[Electrical polarity|polarity]]), was independent of the mass of the charged objects, and followed the [[superposition principle]]. [[Coulomb's law]] unifies all these observations into one succinct statement.<ref name="Coulomb">{{cite journal |first=Charles |last=Coulomb |journal=Histoire de l'Académie Royale des Sciences |year=1784 |title=Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de metal |pages=229–269}}</ref>

Subsequent mathematicians and physicists found the construct of the ''[[electric field]]'' to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical "[[test charge]]" anywhere in space and then using Coulomb's Law to determine the electrostatic force.<ref name=FeynmanVol2/>{{rp|((4-6–4-8))}} Thus the electric field anywhere in space is defined as
<math display="block">\mathbf{E} = {\mathbf{F} \over{q}},</math>
where <math>q</math> is the magnitude of the hypothetical test charge. Similarly, the idea of the ''[[magnetic field]]'' was introduced to express how magnets can influence one another at a distance. The [[Lorentz force|Lorentz force law]] gives the force upon a body with charge <math>q</math> due to electric and magnetic fields:
<math display="block" qid=Q849919>\mathbf{F} = q\left(\mathbf{E} + \mathbf{v} \times \mathbf{B}\right),</math>
where <math> \mathbf{F}</math> is the electromagnetic force, <math> \mathbf{E}</math> is the electric field at the body's location, <math>\mathbf{B}</math> is the magnetic field, and <math> \mathbf{v}</math> is the [[velocity]] of the particle. The magnetic contribution to the Lorentz force is the [[cross product]] of the velocity vector with the magnetic field.<ref>{{Cite book|last=Tonnelat|first=Marie-Antoinette|url=https://www.worldcat.org/oclc/844001|title=The principles of electromagnetic theory and of relativity.|date=1966|publisher=D. Reidel|isbn=90-277-0107-5|location=Dordrecht|oclc=844001|author-link=Marie-Antoinette Tonnelat |page=85}}</ref><ref name="openstax-university-physics2">{{cite book|title=University Physics, Volume 2 |url=https://openstax.org/details/books/university-physics-volume-2 |publisher=[[OpenStax]] |year=2021 |first1=Samuel J. |last1=Ling |first2=Jeff |last2=Sanny |first3=William |last3=Moebs |isbn=978-1-947-17221-0}}</ref>{{rp|482}}

The origin of electric and magnetic fields would not be fully explained until 1864 when [[James Clerk Maxwell]] unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by [[Oliver Heaviside]] and [[Josiah Willard Gibbs]].<ref>{{cite book
|title=Polarized light in liquid crystals and polymers
|first1=Toralf
|last1=Scharf
|publisher=John Wiley and Sons
|year=2007
|isbn=978-0-471-74064-3
|page=19
|chapter=Chapter 2
|chapter-url=https://books.google.com/books?id=CQNE13opFucC&pg=PA19}}</ref> These "[[Maxwell's equations]]" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a [[wave]] that traveled at a speed that he calculated to be the [[speed of light]]. This insight united the nascent fields of electromagnetic theory with [[optics]] and led directly to a complete description of the [[electromagnetic spectrum]].<ref>
{{cite book
 |first=William
 |last=Duffin
 |title=Electricity and Magnetism
 |publisher=McGraw-Hill
 |pages=[https://archive.org/details/electricitymagn00duff/page/364 364–383]
 |year=1980
 |edition=3rd
 |isbn=978-0-07-084111-6
 |url=https://archive.org/details/electricitymagn00duff/page/364
}}</ref>