Boundary-Value Problems

This chapter explains the boundary-value problems of the plane and the cylinder concerning infinite surfaces which serve as guides to traveling waves. The sphere is an example of a body bounded by a closed surface within which there can be set up a system of standing waves. The chapter shows that the field of the principal wave within the conductor tends to concentrate in a thin skin near the surface. The field and current distribution within the cylinder in the case of complementary waves is nearly uniform. The "skin effect" is then external, and the conversion into heat correspondingly large. As the conductivity of the cylinder is decreased, the attenuation of the principal wave increases, while that of the complementary waves is diminished until finally, in the limit of a perfect dielectric cylinder, the authors find the principal wave to have vanished and the complementary waves propagated without attenuation.