Chapter 11: Problem 8
An electric field in free space is given in spherical coordinates as \(\mathbf{E}_{s}(r)=E_{0}(r) e^{-j k r} \mathbf{a}_{\theta} \mathrm{V} / \mathrm{m} .(a)\) Find \(\mathbf{H}_{s}(r)\) assuming uniform plane wave behavior. \((b)\) Find \(<\mathbf{S}>\cdot(c)\) Express the average outward power in watts through a closed spherical shell of radius \(r\), centered at the origin. \((d)\) Establish the required functional form of \(E_{0}(r)\) that will enable the power flow in part \(c\) to be independent of radius. With this condition met, the given field becomes that of an isotropic radiator in a lossless medium (radiating equal power density in all directions).
Short Answer
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