The positivity and other properties of the matrix of capacitance: physical and mathematical implications

Details The positivity and other properties of the matrix of capacitance: physical and mathematical implications The positivity and other properties of the matrix of capacitance: physical and mathematical implications

2009-03-03

arxiv.org/abs/0903.0600v4

Physics

Classical Physics

10 pages, 2 figures, LaTeX2e. More motivations and physical discussions added. Version to appear at Journal of Electrostatics

Scientific paper

We prove that the matrix of capacitance in electrostatics is a positive-singular matrix with a non-degenerate null eigenvalue. We explore the physical implications of this fact, and study the physical meaning of the eigenvalue problem for such a matrix. Many properties are easily visualized by constructing a "potential space" isomorphic to the euclidean space. The problem of minimizing the internal energy of a system of conductors under constraints is considered, and an equivalent capacitance for an arbitrary number of conductors is obtained. Moreover, some properties of systems of conductors in successive embedding are examined. Finally, we discuss some issues concerning the gauge invariance of the formulation.

Affiliated with

Also associated with

No associations

Rating

The positivity and other properties of the matrix of capacitance: physical and mathematical implications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The positivity and other properties of the matrix of capacitance: physical and mathematical implications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The positivity and other properties of the matrix of capacitance: physical and mathematical implications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653912