ISSN:
1089-7550
Quelle:
AIP Digital Archive
Thema:
Physik
Notizen:
The retarded solution to the inhomogeneous wave equation in electrodynamics is studied with a purpose to understand Wu's missile and subsequently the radial dependence of energy transmitted by transient sources. The finite rate of change of the source current is shown to imply the inverse-square law at a sufficiently large distance, the region of which is determined by the minimum scale time tm of the current and may be called the (generalized) Fraunhofer region. With a uniform disk source, the electric field on the symmetry axis for a wide range is shown equal to the difference of the current at two times. Hence, examples with analytic results are given to demonstrate clearly how the pulse energy decreases with distance at a much slower rate in the (generalized) Fresnel region and how the inverse-square dependence is recovered in the farther region. Moreover, Wu's current profile, though with infinite slopes, is a Lighthill's generalized function and missiles refer to the transmitted pulses in the limit of zero tm which gives an infinite Fresnel region. A square temporal profile and other profiles with a sudden rise (or fall), including Samaddar's single-cycled cosine, which also generate missiles with an inverse-linear dependence, are studied. © 1999 American Institute of Physics.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.371598
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