Magnetic Circuit Calculator
The Magnetic Circuit Calculator solves magnetic circuits using Hopkinson's law (Φ = MMF/R), the magnetic analog of Ohm's law. Supports multi-segment series circuits with air gaps, 5 core materials with B-H curves, fringing correction, saturation detection, and interactive SVG circuit schematic. Free, no signup required.
Presets
MMF Source
Circuit Segments
Results
Per-Segment Analysis
Magnetic Circuit Diagram
Material Properties
| Material | Relative Permeability (µr) | Saturation Flux Density |
|---|---|---|
| Silicon Steel (M19) | 4,000 | 2 T |
| Ferrite (MnZn) | 2,000 | 0.4 T |
| Powdered Iron (T-series) | 100 | 1 T |
| Amorphous Metal (Metglas) | 10,000 | 1.56 T |
| Mu-Metal | 50,000 | 0.8 T |
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What is a Magnetic Circuit Calculator?
A magnetic circuit calculator analyzes magnetic flux paths using Hopkinson's law: Φ = MMF/R, which is the magnetic analog of Ohm's law (V = IR). Just as electrical circuits have voltage, current, and resistance, magnetic circuits have magnetomotive force (MMF = NI), magnetic flux (Φ), and reluctance (R = l/µA). This calculator handles multi-segment circuits with different core materials and air gaps, computes per-segment flux density and field intensity, and detects magnetic saturation — essential for transformer, inductor, and actuator core design.
How to Use This Calculator
- Set the MMF source: enter number of turns and current (MMF = N × I)
- Define circuit segments: specify length, cross-section area, and material for each segment
- Add air gaps where needed — the calculator applies fringing correction automatically
- Choose a preset (E-I core, toroid with gap, C-core, pot core) or build a custom circuit
- Review per-segment flux density, field intensity, and saturation status
Frequently Asked Questions
What is Hopkinson's law for magnetic circuits?
Hopkinson's law states Φ = MMF/R, where Φ is magnetic flux (Wb), MMF is magnetomotive force (A·turns), and R is reluctance (A·turns/Wb). It's the magnetic analog of Ohm's law. For series circuits, total reluctance is the sum of individual reluctances, just like series resistances.
Why are air gaps important in magnetic circuits?
Air gaps have much higher reluctance than core material (µr = 1 vs thousands). A small air gap dominates the total circuit reluctance, which linearizes the inductance and prevents core saturation at the cost of lower inductance. Air gaps are essential in inductors and controlled in transformers.
What is magnetic fringing and how does it affect calculations?
Magnetic fringing occurs when flux lines spread out at air gap boundaries, effectively increasing the gap's cross-section area. The fringing factor (typically 1.1-1.3) corrects for this by dividing the gap reluctance. For larger gaps relative to core dimensions, fringing is more significant.
How do I detect and prevent core saturation?
Core saturation occurs when flux density B exceeds the material limit (e.g., 2.0 T for silicon steel, 0.4 T for ferrite). This calculator checks B per segment and flags saturation. To avoid saturation: increase core area, add an air gap, reduce current, or choose a higher-saturation material.
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