Potencials and electric fields inside and outside resistive conductors carrying steady currents / Potenciais e campos eletricos dentro e fora de condutores resistivos com correntes constantes

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

In Chapter 1 we present an introduction about the electric field inside and outside resistive conductors carrying steady currents. We also discuss the distribution of surface charges that maintains the current fiow and its relation with these electric fields. We present some experiments related with these electric fields outside conductors with steady current. Part I of this work deals with long straight conductors. In Chapter 2 we present the treatment of a long cylindrical wire of circular cross section conducting a steady current, already known in the literature. We present some of the methods that we employ in the problems that follow. Chapter 3 deals with the force between an infinite cylindrical conducting shell without current and a point charge close by (inside or outside the shell). This solution is new in the literature. This force of zeroth order (electrostatics) complements the analysis of the first order force (i.e., proportional to the current or to the drifting velocity of the conduction electrons) in the case of the long cylindrical wire with steady current. Chapter 4 deals with the new problem of a long straight wire, still with a steady current, but now with a battery in the middle. Our objective here is to study the behaviour of the fields and of the surface charges near the battery. Chapter 5 presents the known problem of straight plates conducting steady currents. This problem was dealt with by the present author during his Master s Degree. The behaviour of the fields and of the surface charges near the battery in the problem of conductors in the shape of plates is approached in Chapter 6. This is also a new problem in the literature, analogous to the problem treated in Chapter 4. In Chapter 7 we generalize the problem of plates with steady currents utilizing now a strip of finite width. To solve this new problem we utilize elliptic-cylindrical coordinates. With this case we finish our treatment of problems of long and straight conductors, carrying currents in the longitudinal direction. In Part II we treat curved conductors with steady currents in the azimuthal direction. These problems are important because they represent a class of electric circuits in which the current fiows over a closed finite path. Chapter 8 presents the known problem of a conducting cylindrical shell of infinite length carrying a steady current in the azimuthal direction. There is a battery in the shape of aline, parallel to the axis of the shell. This geometry yields a very simple solution with a closed analytical form for the potential, electric field and surface charges, although the cylinder has an infinite length. Chapter 9 presents the new treatment of a resistive spherical shell with a steady current. In this case, the battery has the shape of a segment of line ( a meridian of the sphere). The more complex problem of a conducting toroid with a steady current in the azimuthal direction, also new in the literature, is presented in Chapter 10. These two problems, about the spherical shell and the toroid, represent two situations where there are no infinities in the geometry nor in the conductivity, while the current is confined in a finite space Even the battery is included in the system, so that we obtain naturally the expected behaviour of the fields and of the surface charges near the battery. In Part III we present a discussion of the problems treated here. We demonstrate that for all the analysed cases there is an electric field outside the conductors with steady currents and we obtain their expressions analytically. The behaviours of all cases in which the battery was present were found according to our expectations. The comparisons that we made with experiments of the literature showed that our theoretical results are reasonable and coherent

ASSUNTO(S)

correntes continuas eletric circuits funções harmonicas eletromagnetismo campos eletricos electromagnetism electric fields direct currents laplace s equations electrodynamics circuitos eletricos - corrente continua eletrodinamica

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