Contents
For the stationary magnetic field of a system of ideal conductors minimum theorems are given that are analogues of Thomson's and Dirichlet's principles in electrostatics. Upper and lower bounds for the inductance of an ideal conductor with one hole are derived from the minimum theorems with the aid of Schwarz's inequality. For a torus the theorems with the aid of Schwarz's inequality. For a torus the bounds are compared numerically with the true inductance.
Übersicht
Für das stationäre magnetische Feld einer Sammlung idealer Leiter werden zwei Minimalsätze gegeben, die dem Thomsonschen und dem Dirichletschen Prinzip der Elektrostatik analog sind. Obere und untere Schranke für die Induktivität eines ringartigen idealen Leiters werden aus den Minimalsätzen mit Hilfe der Schwarzschen Ungleichung abgeleitet. Für den Fall eines Torus werden die Schranken numerisch mit der wahren Induktivität verglichen.
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Karlsson, P.W. Inductance inequalities for ideal conductors. Archiv f. Elektrotechnik 67, 29–33 (1984). https://doi.org/10.1007/BF01574728
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DOI: https://doi.org/10.1007/BF01574728