Artigo Publicado em Periódico
Field and electric potential of conductors with fractal geometry
Fecha
2007Registro en:
0953-8984
v. 19, n. 47
Autor
Assis, Thiago Albuquerque de
Mota, Fernando de B.
Miranda, José Garcia Vivas
Andrade, Roberto Fernandes Silva
Castilho, Caio Mário Castro de
Assis, Thiago Albuquerque de
Mota, Fernando de B.
Miranda, José Garcia Vivas
Andrade, Roberto Fernandes Silva
Castilho, Caio Mário Castro de
Institución
Resumen
In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplace's equation subject to the appropriate Dirichlet's condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3−α, where α is the usual roughness exponent. The equipotential surfaces, obtained from Laplace's equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases.