Editing Electric field (section)

=== Point charge in uniform motion ===
The invariance of the form of [[Maxwell's equations]] under [[Lorentz transformation]] can be used to derive the electric field of a uniformly moving point charge. The charge of a particle is considered frame invariant, as supported by experimental evidence.<ref name=":0">{{Cite book |last1=Purcell |first1=Edward M. |url=https://www.cambridge.org/highereducation/books/electricity-and-magnetism/0F97BB6C5D3A56F19B9835EDBEAB087C |title=Electricity and Magnetism |last2=Morin |first2=David J. |date=2013-01-21 |website=Higher Education from Cambridge University Press |isbn=9781139012973 |pages=241–251 |language=en |doi=10.1017/cbo9781139012973 |access-date=2022-07-04}}</ref> Alternatively the electric field of uniformly moving point charges can be derived from the [[Lorentz transformation]] of [[four-force]] experienced by test charges in the source's [[rest frame]] given by [[Coulomb's law]] and assigning electric field and magnetic field by their definition given by the form of [[Lorentz force#Lorentz force law as the definition of E and B|Lorentz force]].<ref>{{Cite book |last1=Rosser |first1=W. G. V. |url=https://link.springer.com/book/10.1007/978-1-4899-6559-2 |title=Classical Electromagnetism via Relativity |year=1968 |isbn=978-1-4899-6258-4 |pages=29–42 |language=en |doi=10.1007/978-1-4899-6559-2}}</ref> However the following equation is only applicable when no acceleration is involved in the particle's history where [[Coulomb's law]] can be considered or symmetry arguments can be used for solving [[Maxwell's equations]] in a simple manner. The electric field of such a uniformly moving point charge is hence given by:<ref>{{Cite book |last=Heaviside |first=Oliver |url=https://en.wikisource.org/wiki/Electromagnetic_effects_of_a_moving_charge |title=Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a moving charge}}</ref>
<math display="block">\mathbf{E} = \frac q {4 \pi \varepsilon_0 r^3}   \frac {1- \beta^2} {(1- \beta^2 \sin^2 \theta)^{3/2}} \mathbf{r} ,</math>
where <math>q</math> is the charge of the point source, <math>\mathbf{r}</math> is the position vector from the point source to the point in space, <math>\beta</math> is the ratio of observed speed of the charge particle to the speed of light and <math>\theta</math> is the angle between <math>\mathbf{r}</math> and the observed velocity of the charged particle. 

The above equation reduces to that given by Coulomb's law for non-relativistic speeds of the point charge. Spherical symmetry is not satisfied due to breaking of symmetry in the problem by specification of direction of velocity for calculation of field. To illustrate this, field lines of moving charges are sometimes represented as unequally spaced radial lines which would appear equally spaced in a co-moving reference frame.<ref name=":0" />