How Far Is the Far Field?

We present a set of formulas for determining the far-field region of a radiator, or scatterer, by examining the integral representation of the magnetic field scattered by a thin straight wire. These formulas are the result of bounding the errors in magnitude and phase of the approximation of the gradient of the free-space Green's function in the far field. Since the error requirements vary from one case to the next, the dependence on them shows that the far field is not a hard-wired parameter, but depends on the sensitivity of a specific case to magnitude and phase errors.