Instead, it is common (e.g. King, 1963) to assume that the medium is homogeneous and isotropic sufficiently far away. In this case, the radiated field asymptotically takes the form of planewaves propagating radially outward (in the O ^ ^ ⁡ ⁡ r direction) with O ^ ^ ⁡ ⁡ r ⋅ ⋅ E = 0 and H = r ^ ^ × × E / Z where Z is the scalar impedance μ μ / ϵ ϵ of the surrounding medium. Then it follows that E 1 × × H 2 = E 1 × × r ^ ^ × × E 2 Z , which by a simple vector identity equals E 1 ⋅ ⋅ E 2 Z r ^ ^ . Similarly, E 2 × × H 1 = E 2 ⋅ ⋅ E 1 Z r ^ ^ and the two terms cancel one another.