Series Magnetic Circuit

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

• 
  

• B is flux density (Wb/m²),

• μ0= 4π×10^−7 (absolute permeability),

• μr is relative permeability (provided or derived from the B-H curve if unknown).

• 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:

• 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= H₁l₁ + H₂l₂ + H₃l₃ + H_gl_g)

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