By M.E. (Morris Edgar) Rose
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Example text
131). Because the field now extends to infinity we must impose condi tions to be satisfied at infinity, as well as on the conducting boundaries, before we can determine unique solutions to the field equations. These conditions are usually known as the "Sommerfeld radiation conditions". We cannot give a thorough discussion of these here, and content ourselves with the following account which draws an analogy with the conditions for uniqueness in electrostatics. The "standard" boundary conditions applied there for a field in two dimensions (and uniform in the z-direction) were K=0(lnr), \E\ = 0(1/r), r-«>.
4 can be used to investigate the transport of energy by the fields we are considering. 3 and the transport of energy is given by eqns. 76-8). 79) that there is no net flow of energy, either toward or away from, the surface, in the region x > 0. 80) and obtain - P _ . 93) since cos 0" = i sinh φ. Since this is a purely imaginary quantity, it implies that there is no transport of energy by the field E", B". Therefore the whole of the energy brought to the surface by the incident ray is carried back into the medium by the reflected ray.
The "tail" of each wave dies out as it runs a short distance up the shore, and each tail runs directly along the shore line as the wave arrives; this is the velocity v/sin 0. The fact that B'\ E" are not zero but decrease exponentially for x < 0 shows that there is slight penetration by the field into the "forbidden" region. 4 can be used to investigate the transport of energy by the fields we are considering. 3 and the transport of energy is given by eqns. 76-8). 79) that there is no net flow of energy, either toward or away from, the surface, in the region x > 0.