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Series Magnetic Circuit

Edwiin

05/28/2025

Definition of Series Magnetic Circuit

Definition: A series magnetic circuit is defined as a magnetic pathway composed of multiple sections with varying dimensions and materials, all carrying the same magnetic field. Consider a circular coil or solenoid with distinct dimensional parameters, as illustrated in the figure below:

Series Magnetic Circuit Analysis

A current I flows through a solenoid with N turns wound around one section of a circular coil, inducing a flux Φ in the core.

a₁, a₂, a₃: Cross-sectional areas of the solenoid sections
l₁, l₂, l₃: Lengths of the three serially connected coil sections with different dimensions
μᵣ₁, μᵣ₂, μᵣ₃: Relative permeabilities of the circular coil materials
a₉, l₉: Area and length of the air gap (assuming ag denotes air gap area)

The total reluctance (S) of the magnetic circuit is:

Procedure for Calculating Total MMF in Series Magnetic Circuits

- Sectionalize the magnetic circuit into distinct parts.
- Determine flux density (B) for each section using $B =ϕ/a$ , where $ϕ$ is flux (Weber) and $a$ is cross-sectional area (m²).
- Calculate magnetizing force (H) using H=B/(μ0μr), where:
  - $B$ is flux density (Wb/m²),
  - $μ_{0} = 4 π \times 1 0^{-7}$ (absolute permeability),
  - μr is relative permeability (provided or derived from the B-H curve if unknown).
- Multiply each H value(e.g., $H1, H2, H3, Hg$ ) by the corresponding section length ( $l1, l2, l3, lg$ ).
- Sum all products of H×l to obtain the total MMF:Total MMF $= H 1 l 1 + H 2 l 2 + H 3 l 3 + H g l g)$

B-H curve for the various material like cast iron, cast steel and sheet steel is shown in the above figure.

Topics

Basic Circuit Theory Circuit Analysis

Edwiin

Hello，I'm Wdwiin. A decade of hands-on experience in electrical engineering, specializing in high-voltage systems, smart grids, and renewable energy technologies. Passionate about technical exchange and knowledge sharing, committed to interpreting industry trends with professional insights to empower peers. Connection creates value—let’s explore the boundless possibilities of the electrical world together!

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