A magnetic circuit approximates a narrow core and its gaps by sections carrying a common magnetic flux . With negligible leakage and approximately uniform magnetic flux density across each section, Gauss's law for magnetism gives . The magnetostatic Ampère law then gives . This requires an appropriate material relation; constant magnetic permeability is an approximation for an actual magnetic core.
A rod of magnetic path length and tangential magnetization closed by a gap of width has constant flux in the one-dimensional magnetic circuit approximation. Equal cross sections and negligible leakage give , while absence of free current gives . Their solution is the displayed pair. Gap fringing or an unspecified cross-section change requires a more detailed field model.
A uniform-radius magnetic arc of length and radius , two linear tapers of length to radius , and an unfringed vacuum gap of length have the displayed gap field. Here and . Tapering concentrates flux, but at fixed winding current the gap-dominated limit is regardless of pole area. Saturation and leakage prevent unrestricted field enhancement.
Magnetic fringing is the spreading of magnetic field lines near an air gap or pole edge, so the gap's effective magnetic flux area exceeds its geometrical pole-face area. A gap much shorter than its transverse dimensions permits a leading uniform-field approximation. High core magnetic permeability does not by itself justify neglecting magnetic fringing for a wide gap.
The magnetic reluctance of a linear section of magnetic circuit is the ratio of the winding's integrated magnetic field intensity to the magnetic flux, with units . For uniform length , cross-sectional area , and relative magnetic permeability , . Series sections carrying the same magnetic flux have additive magnetic reluctances, and .
For a uniform core of path length , a narrow air gap , and winding turns, Ampère's circuital law gives when leakage and fringing are negligible. If a reversible branch has differential magnetic permeability , linearization gives . An offset in the operating branch changes the bias field, not this differential formula. For at the origin, .
For a linear-radius taper from to over length , constant absolute permeability , and a common approximately axial flux, integrate to obtain the displayed reluctance. Leakage, fringing, nonuniform transverse fields and saturation limit this one-dimensional magnetic-circuit approximation.
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A magnetic circuit is a conceptual framework used to analyze the magnetic behavior of materials and devices, analogous to an electrical circuit. In a magnetic circuit, the flow of magnetic flux is compared to the flow of electric current in an electrical circuit. Here are the key components and concepts associated with magnetic circuits: 1. **Magnetic Flux (Φ)**: This is the measure of the quantity of magnetism, considering the strength and the extent of a magnetic field.