Método de Hertz para solucionar las ecuaciones de Maxwell: El caso del dipolo oscilante
Keywords:
Dipolo oscilante, Potenciales de Hertz, Método de Hertz para solucionar las ecuaciones de Maxwell, ecuaciones de Maxwell (es)Downloads
A finales del siglo XIX Hertz propuso un método muy original para solucionar las ecuaciones de Maxwell, en términos de los llamados potenciales de Hertz (Πe, Πm), que simetrizan las ecuaciones de Maxwell. Al aplicar este método a la solución del dipolo oscilante los potenciales de Hertz se relacionan con una única magnitud escalar Q, que es proporcional al flujo eléctrico. Esto permite expresar el campo electromagnético (E,H) en términos del flujo eléctrico únicamente, llevando así a una visión alternativa del campo emitido por el dipolo. Con fines pedagógicos este artículo describe el método de Hertz, que es poco conocido, y además, describe el proceso para construir las gráficas de las líneas de campo eléctrico, obtenidas por Hertz por primera vez; adicionalmente se presentan las líneas del campo magnético emitido por el dipolo.
By the end of the 19th century, Hertz developed an original procedure for the solution of Maxwell equations. He introduced the so-called Hertz potentials (Πe, Πm), which have the very interesting property of making Maxwell equations symmetrical. Application of Hertz’s method to the solution of the oscillating electric dipole is based on a scalar function Q, which is proportional to the electric flux. In this way, the electromagnetic field (E,H) becomes a function of electric flux only. For its pedagogical value, in this paper we describe Hertz’s method, which is neither widely known, nor easily available to most students and researchers. Additionally, we describe in some detail Hertz’s procedure to build the graphs of the electric field (the latter were obtained by Hertz for the first time, and are reproduced in many intermediate textbooks without any explanation), and present the companion graphs for the magnetic field associated with the dipole.
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