Editing Newton's laws of motion (section)

===Electromagnetism===
Newton's three laws can be applied to phenomena involving [[electricity]] and [[magnetism]], though subtleties and caveats exist.

[[Coulomb's law]] for the electric force between two stationary, [[electric charge|electrically charged]] bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge <math>q_1</math> exerts upon a charge <math>q_2</math> is equal in magnitude to the force that <math>q_2</math> exerts upon <math>q_1</math>, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law.<ref>{{Cite journal|last=Kneubil|first=Fabiana B.|date=2016-11-01|title=Breaking Newton's third law: electromagnetic instances|url=https://iopscience.iop.org/article/10.1088/0143-0807/37/6/065201|journal=[[European Journal of Physics]] |volume=37|issue=6|pages=065201|doi=10.1088/0143-0807/37/6/065201|bibcode=2016EJPh...37f5201K |s2cid=126380404 |issn=0143-0807}}</ref>

Electromagnetism treats forces as produced by ''fields'' acting upon charges. The [[Lorentz force law]] provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration.<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}}</ref>{{Rp|page=85}} According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge <math>q</math> and to the strength of the electric field. In addition, a ''moving'' charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector [[cross product]],<math display="block">\mathbf{F} = q \mathbf{E} + q \mathbf{v} \times \mathbf{B}.</math>
[[Image:Cyclotron_motion.jpg|right|thumb|The Lorentz force law in effect: electrons are bent into a circular trajectory by a magnetic field.]]If the electric field vanishes (<math>\mathbf{E} = 0</math>), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a [[helix]]) around the magnetic field lines at the [[Cyclotron motion|cyclotron frequency]] <math>\omega = qB/m</math>.<ref name=":4">{{Cite book|last=Reichl|first=Linda E.|url=https://www.worldcat.org/oclc/966177746|title=A Modern Course in Statistical Physics|date=2016|publisher=Wiley-VCH|isbn=978-3-527-69048-0|edition=4th|location=Weinheim, Germany|oclc=966177746|author-link=Linda Reichl}}</ref>{{Rp|page=222}} [[Mass spectrometry]] works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the [[mass-to-charge ratio]].<ref>{{Cite book |last1=Chu |first1=Caroline S. |chapter=Introduction to Modern Techniques in Mass Spectrometry |date=2010 |chapter-url=https://doi.org/10.1007/978-1-60327-233-9_6 |title=Biomedical Applications of Biophysics |pages=137–154 |editor-last=Jue |editor-first=Thomas |place=Totowa, NJ |publisher=Humana Press |language=en |doi=10.1007/978-1-60327-233-9_6 |isbn=978-1-60327-233-9 |access-date=2022-03-24 |last2=Lebrilla |first2=Carlito B.}}</ref>

Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the electromagnetic field is proportional to the [[Poynting vector]].<ref name="Panofsky1962"/>{{Rp|184}}<ref>{{Cite journal |last1=Bonga |first1=Béatrice |last2=Poisson |first2=Eric |last3=Yang |first3=Huan |date=November 2018 |title=Self-torque and angular momentum balance for a spinning charged sphere |url=http://aapt.scitation.org/doi/10.1119/1.5054590 |journal=[[American Journal of Physics]] |language=en |volume=86 |issue=11 |pages=839–848 |doi=10.1119/1.5054590 |arxiv=1805.01372 |bibcode=2018AmJPh..86..839B |s2cid=53625857 |issn=0002-9505}}</ref>

There is subtle conceptual conflict between electromagnetism and Newton's first law: [[Maxwell's equations|Maxwell's theory of electromagnetism]] predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the [[speed of light]] and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of ''space'' and ''time'' in such a way that all inertial observers will agree upon the speed of light in vacuum.{{refn|group=note|Discussions can be found in, for example, Frautschi et al.,<ref name=":0" />{{Rp|page=215}} Panofsky and Phillips,<ref name="Panofsky1962">{{Cite book|last1=Panofsky|first1=Wolfgang K. H.|url=https://www.worldcat.org/oclc/56526974|title=Classical Electricity and Magnetism|last2=Phillips|first2=Melba|date=2005|publisher=Dover Publications|isbn=0-486-43924-0|edition=2nd|location=Mineola, N.Y.|oclc=56526974|author-link=Wolfgang Panofsky|author-link2=Melba Phillips|orig-date=1962}}</ref>{{Rp|page=272}} Goldstein, Poole and Safko,<ref name=":6">{{Cite book |last1=Goldstein |first1=Herbert |author-link=Herbert Goldstein |title-link=Classical Mechanics (Goldstein) |title=Classical Mechanics |last2=Poole |first2=Charles P. |last3=Safko |first3=John L. |date=2002 |publisher=Addison Wesley |isbn=0-201-31611-0 |edition=3rd |location=San Francisco |oclc=47056311}}</ref>{{Rp|page=277}} and Werner.<ref>{{Cite journal |last=Werner |first=Reinhard F. |date=2014-10-09 |title=Comment on "What Bell did" |journal=[[Journal of Physics A: Mathematical and Theoretical]] |volume=47 |issue=42 |pages=424011 |bibcode=2014JPhA...47P4011W |doi=10.1088/1751-8113/47/42/424011 |s2cid=122180759 |issn=1751-8113}}</ref>}}