Phase Portraits and Critical Elements of Magnetic Fields Generated by a Piecewise Rectilinear Electric Circuits (original) (raw)

Lagrange and Finsler Geometry, 1996

Abstract

In §1 the basic notions of the theory of phase portraits and critical elements of magnetic fields are presented; §2 and §3 describe the symmetries of phase portraits and of the critical points sets respectively, for the magnetic field generated by unitary currents which traverse coplanar angular wires. §4 presents computer experiments. In §5, the associated magnetic field lines are shown to be solutions of a potential conservative system, and also geodesics for a certain Riemannian metric on the space surrounding the wires.

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