In terms of the scalar and vector potentials, this last equation becomes:
For a given charge and current distribution, and , the solutions to these equations in SI units are
where is the retarded time. This is sometimes also expressed with , where the square brackets are meant to indicate that the time should be evaluated at the retarded time. Of course, since the above equations are simply the solution to an inhomogeneousdifferential equation, any solution to the homogeneous equation can be added to these to satisfy the boundary conditions. These homogeneous solutions in general represent waves propagating from sources outside the boundary.
When the integrals above are evaluated for typical cases, e.g. of an oscillating current (or charge), they are found to give both a magnetic field component varying as (the induction field) and a component decreasing as (the radiation field).
Rindler, Wolfgang (1991). Introduction to Special Relativity (2nd). Oxford: Oxford University Press. ISBN 0-19-853952-5.
Jackson, J D (1999). Classical Electrodynamics (3rd). New York: Wiley. ISBN ISBN 0-471-30932-X.