2020/07/31 by Ivica Smolić, Bruno Klajn
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Capacitance #Capacitor #Composite Material Mechanics #Composite material #Diagonal #Electrical conductor #Electrical engineering #Electrode #Electromagnetic Scattering and Analysis #Engineering #Geometry #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Quantum mechanics #Voltage #math-ph #math.MP #physics.class-ph
paper · pdf · doi:10.2528/pierb21011501
published as Progress In Electromagnetics Research B, Vol. 92, 1-18, 2021 · ver. 2: 18 pages, 7 figures; minor revision, accepted for publication in PIER B
openalex publication_date 2021/01/01 · arxiv created 2021/03/11 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The capacitance matrix relates potentials and charges on a system of conductors. We review and rigorously generalize its properties, block-diagonal structure and inequalities, deduced from the geometry of system of conductors and analytic properties of the permittivity tensor. Furthermore, we discuss alternative choices of regularization of the capacitance matrix, which allow us to find the charge exchanged between the conductors having been brought to an equal potential. Finally, we discuss the tacit approximations used in standard treatments of the electric circuits, demonstrating how the formulae for the capacitance of capacitors connected in parallel and series may be recovered from the capacitance matrix.