TITLE:
Replacing Biot-Savart Rule of Magnetic Field by a “Magnetic Auvert Rule” to Evaluate Field Surfaces and Field Curves around Circular and Square Current Loops Modeled as Electrical Segments
AUTHORS:
Geoffroy Auvert
KEYWORDS:
Biot-Savart Law, Magnetic Auvert Rule, Magnetic Surface, Magnetic Field Line, Magnetic Field Curve, Electrical Segment, Scalar Field, Right-Hand Rule
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.8,
August
26,
2026
ABSTRACT: Around a straight wire carrying a steady current, magnetic field lines are classically represented by concentric circles, each point on a given circle having the same field magnitude. For finite electrical segments, the Biot-Savart law is normally used to compute and plot these curves, but that approach becomes cumbersome for complex wire geometries. The author proposes replacing the Biot-Savart formulation with a new Magnetic Auvert rule to evaluate a scalar magnetic potential and the corresponding magnetic field vectors. This rule makes it possible to compute and draw magnetic field lines and surfaces for arbitrary geometries composed of fixed electrical segments, enabling field visualization around circular, square, and more general current configurations.