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The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplaces equation that is accessible for an intermediate course on electricity and magnetism. The properties of Laplaces equation permits to prove many properties of the capacitance matrix. Some examples are given to illustrate the usefulness of such properties.
In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplac
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem starting
The geodesic has a fundamental role in physics and in mathematics: roughly speaking, it represents the curve that minimizes the arc length between two points on a manifold. We analyze a basic but misinterpreted difference between the Lagrangian that
In the first sections of this article, we discuss two variations on Maxwells equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equa
I had the marvelous good fortune to be Ken Wilsons graduate student at the Physics Department, Cornell University, from 1972 to 1976. In this article, I present some recollections of how this came about, my interactions with Ken, and Cornell during t