Investigación

 

The random walk of an electrostatic field using parallel infinite charged planes

 

R. Aldana^a, J. Vidal Alcalá^b, and G. González^c,d

 

^a Instituto Tecnológico y de Estudios Superiores de Occidente, Periférico Sur Manuel Gómez Morín 8585 C.P. 45604, Tlaquepaque, Jal., México.

^b CIMAT y Cátedras CONACYT, Periférico Norte 13615, 97119 Mérida, Yucatán, México.

^c Cátedras CONACYT, Universidad Autónoma de San Luis Potosí, San Luis Potosí, 78000 México. e-mail: gabriel.gonzalez@uaslp.mx

^d Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, San Luis Potosí, 78000 México.

 

Received 28 October 2014;
accepted 19 January 2015

 

Abstract

We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either ±ó. We formulate the problem of this stochastic process by using a rate equation for the most probable value for the electrostatic field subject to the appropriate transition probabilities according to the electrostatic boundary conditions. Our model gives rise to a stochastic law when the charge distribution is not deterministic. The probability distribution of the electrostatic field intensity, the mean value of the electrostatic force and the energy density are obtained.

Keywords: Random walk in random media; Markov chain; electrostatic field.

 

PACS: 41.20.Cv; O5.40.-a

 

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