The Kirchhoff gauge
نویسنده
چکیده
We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge. PACS: 03.50.De, 03.50.Kk, 41.20.-q
منابع مشابه
Computing the additive degree-Kirchhoff index with the Laplacian matrix
For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.
متن کاملOn nonlocal elliptic system of $p$-Kirchhoff-type in $mathbb{R}^N$
Using Nehari manifold methods and Mountain pass theorem, the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.
متن کاملSemi-Analytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation
Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are ...
متن کاملMultiplicity result to some Kirchhoff-type biharmonic equation involving exponential growth conditions
In this paper, we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity. Using some variational arguments and exploiting the symmetries of the problem, we establish a multiplicity result giving two nontrivial solutions.
متن کاملThe Laplacian Polynomial and Kirchhoff Index of the k-th Semi Total Point Graphs
The k-th semi total point graph of a graph G, , is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of edge considered. In this paper, a formula for Laplacian polynomial of in terms of characteristic and Laplacian polynomials of G is computed, where is a connected regular graph.The Kirchhoff index of is also computed.
متن کامل