By Edwin Bidwell Wilson

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The product of jzext and the cross-section area of the cylinder is finite. It is called the line current density and has the only component Iz , independent of the cross-section shape. The fields are infinite near the line current. They are found from the Maxwell equations in which jz is proportional to δ(r ), so that the integral of jz over any part of the surface z = const containing the point r = 0, is finite and equal to Izext . The fields depend neither on z nor on the azimuthal coordinate ϕ, and have only the components H ϕ and Ez .

The amplitudes of these waves are found from the demand that the sum of their fields equals the given field. 19), both these amplitudes are equal to 1/2. The fields of the eigenwaves at z > 0 are obtained from the fields at z = 0 by multiplying by exp(−ihrg z) and exp(−ihlf z), respectively, so that the resulting field has the components 1 [exp(−ihpg z) + exp(−ihlf z)], 2 i Ey (z) = [exp(−ihpg z) − exp(−ihlf z)]. 2 √ Since hrg + hlf = 2k εµ, hrg − hlf = −2kκ , we have Ex ( z ) = √ Ex (z) = exp(−ik εµz) cos(κ z), √ Ey (z) = exp(−ik εµz) sin(κ z).

82) are necessary and sufficient for the line on which some components of the fields become infinite, not to be a linear source, but an edge. Below we show that if these conditions hold, then the energy flux out of the line is zero. 82) the equality to zero of the energy flux is only necessary (but not sufficient) for the line to be an edge. In certain cases it is valid for a linear source, too. 82) violates. 82) holds, we find the field structure near the edge. 4). Align the z-axis of the cylindrical coordinate system along the wedge edge.

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