Editing Magnetic field (section)

==== Propagation of Electric and Magnetic fields ====
[[Special relativity|Special theory of relativity]] imposes the condition for events related by [[Causality|cause and effect]] to be time-like separated, that is that causal efficacy propagates no faster than light.<ref>{{Cite book |author=Naber, Gregory L. |url=http://worldcat.org/oclc/804823303 |title=The Geometry of Minkowski spacetime : an introduction to the mathematics of the special theory of relativity |date=2012 |publisher=Springer |isbn=978-1-4419-7837-0 |pages=4–5 |oclc=804823303}}</ref> [[Maxwell's equations]] for electromagnetism are found to be in favor of this as electric and magnetic disturbances are found to travel at the speed of light in space. Electric and magnetic fields from classical electrodynamics obey the [[principle of locality]] in physics and are expressed in terms of retarded time or the time at which the cause of a measured field originated given that the influence of field travelled at speed of light. The retarded time for a point particle is given as solution of:

<math display="block">t_r = \mathbf{t} - \frac{\left|\mathbf{r} - \mathbf{r}_s(t_r)\right|}{c}</math>

where <math display="inline">t_r</math> is [[retarded time]] or the time at which the source's contribution of the field originated, <math display="inline">r_s(t)</math> is the position vector of the particle as function of time, <math display="inline">\mathbf{r}</math> is the point in space, <math display="inline">\mathbf{t}</math> is the time at which fields are measured and <math display="inline">c</math> is the speed of light. The equation subtracts the time taken for light to travel from particle to the point in space from the time of measurement to find time of origin of the fields. The uniqueness of solution for <math display="inline">t_r</math> for given <math>\mathbf{t}</math>, <math>\mathbf{r}</math> and <math>r_s(t)</math> is valid for charged particles moving slower than speed of light.<ref name="Rosser1968"/>