Coulomb's law can be used to gain insight into the form of the magnetic field generated by moving charges since by special relativity, in certain cases the magnetic field can be shown to be a transformation of forces caused by the electric field. When no acceleration is involved in a particle's history, Coulomb's law can be assumed on any test particle in its own inertial frame, supported by symmetry arguments in solving Maxwell's equation, shown above. Coulomb's law can be expanded to moving test particles to be of the same form. This assumption is supported by Lorentz force law which, unlike Coulomb's law is not limited to stationary test charges. Considering the charge to be invariant of observer, the electric and magnetic fields of a uniformly moving point charge can hence be derived by the Lorentz transformation of the four force on the test charge in the charge's frame of reference given by Coulomb's law and attributing magnetic and electric fields by their definitions given by the form of Lorentz force. The fields hence found for uniformly moving point charges are given by: E = q 4 π π ϵ ϵ 0 r 3 1 − − β β 2 ( 1 − − β β 2 sin 2 ⁡ ⁡ θ θ ) 3 / 2 r B = q 4 π π ϵ ϵ 0 r 3 1 − − β β 2 ( 1 − − β β 2 sin 2 ⁡ ⁡ θ θ ) 3 / 2 v × × r c 2 = v × × E c 2 where q is the charge of the point source, r is the position vector from the point source to the point in space, v is the velocity vector of the charged particle, β β is the ratio of speed of the charged particle divided by the speed of light and θ θ is the angle between r and v .