Editing Magnetism (section)

== Interpretation of magnetism by means of relative velocities ==

In the years after 1820, [[André-Marie Ampère]] carried out numerous experiments in which he measured the forces between direct currents. In particular, he also studied the magnetic forces between non-parallel wires.<ref>{{cite book | last=Assis | first=A. K. T. | author2=J. P. M. C. Chaib | title = Ampère's electrodynamics: Analysis of the meaning and evolution of Ampère's force between current elements, together with a complete translation of his masterpiece: Theory of electrodynamic phenomena, uniquely deduced from experience | publisher = C. Roy Keys Inc. | year = 2015 | isbn = 978-1-987980-03-5}}</ref> The final result of his work was a force law that is now named after him. In 1835, [[Carl Friedrich Gauss]] realized <ref name="Gauss1835">{{cite book | last = Gauss | first = Carl Friedrich | title = Carl Friedrich Gauss Werke. Fünfter Band | publisher = Königliche Gesellschaft der Wissenschaften zu Göttingen | year = 1867 | page = 617}}</ref> that [[Ampere's force law]] in its original form can be explained by a generalization of [[Coulomb's law]]. 

Gauss's force law states that the electromagnetic force <math display="inline">\mathbf{F}_1</math> experienced by a point charge, <math>q_1</math> with trajectory <math>\mathbf{r}_1(t)</math>, in the vicinity of another point charge, <math>q_2</math> with trajectory <math>\mathbf{r}_2(t)</math>, in a vacuum is equal to the [[central force]]
: <math>\mathbf{F}_1 = \frac{q_1\,q_2}{4\,\pi\,\epsilon_0}\,\frac{\mathbf{r}}{|\mathbf{r}|^3}\,\left(1 + \frac{|\mathbf{v}|^2}{c^2} - \frac{3}{2}\,\left(\frac{\mathbf{r}}{|\mathbf{r}|}\cdot\frac{\mathbf{v}}{c}\right)^2\right)</math>,
where <math display="inline">\mathbf{r} = \mathbf{r}_1(t) - \mathbf{r}_2(t)</math> is the distance between the charges and <math display="inline">\mathbf{v} = \dot{\mathbf{r}}_1(t) - \dot{\mathbf{r}}_2(t)</math> is the relative velocity. [[Wilhelm Eduard Weber]] confirmed Gauss's hypothesis in numerous experiments.<ref>{{cite book | title = Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume I: Gauss und Weber's Absolute System of Units | author = Wilhelm Weber |	publisher = Apeiron Montreal | editor = Andre Koch Torres Assis | year = 2021}}</ref><ref>{{cite book | title = Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume II: Weber's Fundamental Force and the Unification of the Laws of Coulomb, Ampere and Faraday | author = Wilhelm Weber |	publisher = Apeiron Montreal | editor = Andre Koch Torres Assis | year = 2021}}</ref><ref>{{cite book | title = Wilhelm Weber's Main Works in Electrodynamics Translated into English. Volume III: Measurement of Weber's Constant c, Diamagnetism, the Telegraph Equation and the Propagation of Electric Waves at Light Velocity | author = Wilhelm Weber |	publisher = Apeiron Montreal | editor = Andre Koch Torres Assis | year = 2021}}</ref> By means of [[Weber electrodynamics]] it is possible to explain the static and quasi-static effects in the non-relativistic regime of classical electrodynamics without [[magnetic field]] and [[Lorentz force]].

Since 1870, [[Maxwell electrodynamics]] has been developed, which postulates that electric and magnetic fields exist. In Maxwell's electrodynamics, the actual electromagnetic force can be calculated using the Lorentz force, which, like the Weber force, is speed-dependent. However, Maxwell's electrodynamics is not fully compatible with the work of Ampère, Gauss and Weber in the quasi-static regime. In particular, Ampère's original force law and the [[Biot-Savart law]] are only equivalent if the field-generating conductor loop is closed.<ref>{{cite book | last=Maxwell | first=James Clerk | title = Treatise on Electricity and Magnetism. Volume 2 | publisher = The Clarendon Press, Oxdord | year = 1881 | edition = 2 | volume = 2 | page = 162}}</ref> Maxwell's electrodynamics therefore represents a break with the interpretation of magnetism by Gauss and Weber, since in Maxwell's electrodynamics it is no longer possible to deduce the magnetic force from a central force.