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How to use a to find permeability for non-linear materials? magnetic circuits problems and solutions pdf

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To solve these problems, it is helpful to use the "Electric-Magnetic Analogy" where magnetic parameters correspond to electrical ones: Magnetic Quantity Electric Analogy MMFcap M cap M cap F Ampere-turns ( ATcap A cap T EMF (Voltage) Magnetic Flux Reluctance Resistance ( Permeability Conductivity ( 2. Essential Equations MMF Equation : is turns and is current). Hopkinson's Law (Ohm's Law for Magnetism) : Reluctance : μ0mu sub 0 (permeability of free space) = μrmu sub r (relative permeability) is material-specific. Flux Density : (measured in Tesla, Magnetic Field Intensity : 3. Solved Problem: Composite Circuit with Air Gap Problem: An iron ring with a cross-sectional area of and mean circumference ( air gap is cut into it. If the relative permeability ( μrmu sub r ) of the iron is , find the current ( ) needed to establish a flux of Step 1: Calculate Reluctances Hopkinson's Law (Ohm's Law for Magnetism) : Reluctance

Same core as above, but a 1 mm air gap is cut. Find the flux and the MMF drop across the gap. Neglect fringing.

$$ l_iron = 80 , \textcm - 0.1 , \textcm = 79.9 , \textcm = 0.799 , \textm $$ (Note: Usually the gap width is subtracted, though at $1 \textmm$ it is often negligible for length, but we calculate precisely here). $$ A = 5 \times 10^-4 , \textm^2 $$ $$ \mu_iron = 800 \times 4\pi \times 10^-7 $$