from the point source to the point in space, is the velocity vector of the charged particle, is the ratio of speed of the charged particle divided by the speed of light and is the angle between and . This form of magnetic field can be shown to satisfy maxwell's laws within the constraint of particle being non accelerating. Note that the above reduces to Biot-Savart law for non relativistic stream of current (). Formally, special relativity combines the electric and magnetic fields into a rank-2 tensor, called the electromagnetic tensor. Changing reference frames mixes these components. This is analogous to the way that special relativity mixes space and time into spacetime, and mass, momentum, and energy into four-momentum. Similarly, the energy stored in a magnetic field is mixed with the energy stored in an electric field in the electromagnetic stress–energy tensor. Magnetic vector potential In advanced topics such as quantum mechanics and relativity it is often easier to work with a potential formulation of electrodynamics rather than in terms of the electric and magnetic fields. In this representation, the magnetic vector potential , and the electric scalar potential , are defined using gauge fixing such that: . The vector potential, given by this form may be interpreted as a generalized potential momentum per unit charge just as is interpreted as a generalized potential energy per unit charge. There are multiple choices one can make for the potential fields that satisfy the above condition. However, the choice of potentials is represented by its respective gauge condition. Maxwell's equations when expressed in terms of the potentials in Lorentz gauge can be cast into a form that agrees with special relativity. In relativity, together with forms a four-potential regardless of the gauge condition, analogous to the four-momentum that combines the momentum and energy of a particle. Using the four potential instead of the electromagnetic tensor has the advantage of being much simpler—and it can be easily modified to work with quantum mechanics. Propagation of Electric and Magnetic fields Special theory of relativity imposes the condition for events related by cause and effect to be time-like separated, that is that causal efficacy propagates no faster than light. 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