(2)

The electric field separates into far- and near-field terms, but the equation for the magnetic field, the defining equation of the potential, does not separate. If we substitute the free-space Green’s function from Eq. (3)

  (3)

into Eq. (2), expand, and gather terms, we can determine the fields directly from the electric currents and eliminate the use of a vector potential.

    (4)

   (5)

Terms with 1/R dependence are the far-field terms. The radiative near-field terms have 1/R2 dependence and near-field terms have 1/R3 dependence. The impedance of free space, η, is 376.7 . We can rearrange Eqs. (4) and (5) so that they become the integral of the dot product of the current density J with dyadic Green’s functions.

It is only a notation difference that leads to a logic expression. Except for a few examples given below, we leave the use of these expressions to numerical methods when designing antennas.