J. A. Hernandes

The potential, electric field and surface charges for a resistive long straight strip carrying a steady current

We consider a long resistive straight strip carrying a constant current and calculate the potential and electric field everywhere in space and the density of surface charges along the strip. We compare these calculations with experimental results.

The internal and external electric fields for a resistive toroidal conductor carrying a steady poloidal current

We consider the case of a resistive toroidal conductor carrying a steady current in the poloidal direction. We obtain algebraic expressions for the electric potential, the electric field and the surface charges inside and outside the toroidal shell. We use toroidal coordinates, in which Laplace’s equation is R-separable. We analyze the limiting case of a thin toroid, which can be compared with the solution for the ideal straight solenoid.

Telegraphy equation from Weber's electrodynamics

We derive the telegraphy equation according to Webers electrodynamics for signal propagating along a very long bidimensional wire in the shape of a rectangular strip of zero thickness. We also derive this equation for a twin lead composed by two of these parallel very long bidimensional wires facing each other. We compare this result with classical electromagnetism.

Surface charges and external electric field in a toroid carrying a steady current

We solve the problem of a resistive toroid carrying a steady azimuthal current. We use standard toroidal coordinates, in which case Laplace’s equation is R-separable. We obtain the electric potential inside and outside the toroid, in two separate cases: 1) the toroid is solid; 2) the toroid is hollow (a toroidal shell). Considering these two cases, there is a difference in the potential inside the hollow and solid toroids. We also present the electric field and the surface charge distribution in the conductor due to this steady current. These surface charges generate not only the electric field that maintains the current flowing, but generate also the electric field outside the conductor. The problem of a toroid is interesting because it is a problem with finite geometry, with the whole system (including the battery) contained within a finite region of space. The problem is solved in an exact analytical form. We compare our theoretical results with an experimental figure demonstrating the existence of the electric field outside the conductor carrying steady current.

Surface Charges in Conductor Plates Carrying Constant Currents

In this work we analyze the case of resistive conductor plates carrying constant currents, utilizing surface charge distributions. We obtain the electric potential in the plates and in the space surrounding them. We obtain a non-vanishing electric field outside the conductors. We compare the theoretical results with experimental data present in the literature.

Surface charges and fields in stationary conductors with steady currents

Is there a force between an external stationary charge and a resistive stationary conductor carrying a steady current? The answer to this question is positive. In this work we present the main results of this interaction. We present experiments published in the literature which measured these effects. We also show the analytical solution for the most common situations, namely: straight wires, strips and toroidal conductors. This force is due to charges spread along the surface of the current carrying conductor. This distribution of surface charges is maintained by the battery, and keep the current flowing along the conductor. This had been pointed out by Kirchhoff and Weber. These surface charges keep the potential gradient along the resistive circuit. They also create an electric field inside and outside the conductor. With this approach we show that there are no fundamental differences between electrostatics and current‐carrying conductors.

POTENTIAL, ELECTRIC FIELD AND SURFACE CHARGES CLOSE TO THE BATTERY FOR A RESISTIVE CYLINDRICAL SHELL CARRYING A STEADY LONGITUDINAL CURRENT

In this work we consider a long, resistive cylindrical shell carrying a steady current. A battery in the middle of the wire generates the current. We study the behavior of the potential, electric field and surface charges close to the battery.