Classical Electrodynamics · Problem 6.12

Plane Electromagnetic Waves and Wave Propagation — John David Jackson

Physics — E&M · admittance-complex-poynting-theorem

Problem

Consider the definition of the admittance Y=G−iBY = G - iB of a two-terminal linear passive network in terms of field quantities by means of the complex Poynting theorem of Section 6.9. (a) By considering the complex conjugate of (6.134) obtain general expressions for the conductance GG and susceptance BB for the general case including radiation loss. (b) Show that at low frequencies the expressions equivalent to (6.139) and (6.140) are G≈1∣Vi∣2∫Vσ ∣E∣2 d3xG \approx \frac{1}{|V_i|^2}\int_V \sigma\,|\mathbf{E}|^2\, d^3x B≈−4ω∣Vi∣2∫V(wm−we) d3xB \approx -\frac{4\omega}{|V_i|^2}\int_V (w_m - w_e)\, d^3x

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