Abstract

AbstractIn this chapter, the exact formulas are derived for the transient fields generated by a horizontal electric dipole with delta function excitation and Gaussian excitation on the plane boundary between two dielectrics. With the delta function excitation, the tangential electric fields consist of a delta function pulse travelling in the air with the velocity c, the oppositely directed delta function pulse travelling in the dielectric with the velocity \( c/\varepsilon ^{1/2} \) for the component E ρ and the velocity \( c\varepsilon ^{1/2} \) for the component E ϕ, and the final static electric field due to the charge left on the dipole. The appearance of the vertical magnetic field is similar to that of the tangential electric field. It is pointed out that the amplitude of the pulsed field along the boundary is \( 1/\rho ^2 \) , which is characteristic of the lateral pulse. With the Gaussian excitation, the final exact formulas for the transient field are expressed in terms of several fundamental functions and finite integrals, which can be evaluated easily. KeywordsElectric DipolePlane BoundaryExact FormulaGaussian PulseStep DiscontinuityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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