Application of the Gibbs Magnetodynamic Principle to Calculation of the Distribution of Direct Currents in Solid Bodies

Abstract

The thermodynamic hypothesis of Gibbs allowing to solve a problem by means of the magnetic principle of virtual works is applied to finding of equilibrium distribution of superficial and volume stationary currents in a continuous body. The variation of magnetic energy is considered with the additional conditions defining constancy of currents, two of which having a differential appearance are necessary and sufficient for the solution of a task in case of a one-coherent body. If the considered body two-coherent (torus, a thick ring) appears one more condition is necessary. In work it is shown what this condition which is also providing uniqueness of the decision can be or constancy of the current proceeding through cross section a torus, or a task of a constant stream of magnetic induction through an opening a torus. At problem definition the first option as more evident was chosen. The problem is solved with the help of a method of Lagrange multipliers. The main received result is that circumstance that induction of magnetic field and volume current in volume address in zero. Thus, magnetic field together with currents is squeezed out on a surface. Communication of the received results with Meissner --- Ochsenfeld effect and the London’s equation applied in the theory of superconductivity and also a problem of communication of molecular currents and currents of conductivity are discussed