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Technology / Technical guide
Inductor Air Gaps: Magnetic Reluctance and Stored Energy
An air gap changes a magnetic circuit’s reluctance and the distribution of stored field energy. Its effect cannot be described simply as more gap means more energy. The result depends on what remains fixed, including current, turns, flux density and magnetic geometry.
Compare the same excitation condition before interpreting gap energy.
A uniform linear magnetic-circuit example separates fixed-flux and fixed-current comparisons without specifying a practical inductor design.
01 / Magnetic path
A low-permeability region changes the field relationship.
A simplified core path can contain a high-permeability material and a gap with permeability approximately µ0.
A simplified core path can contain a high-permeability material and a gap with permeability approximately µ0. For the same flux density, the gap requires a larger field strength than an ideal high-permeability section. It can therefore carry a substantial part of the magnetomotive-force requirement.
Magnetics describes discrete and distributed-gap concepts in its inductor reference. These describe different ways of introducing lower-permeability regions into a magnetic path. They do not establish that every inductor uses the same geometry or that any MARSTON converter contains one of those constructions.
02 / Reluctance model
Geometry enters through a declared idealisation.
For a uniform gap of length g and area A, neglecting fringing, the gap reluctance is Rg = g/(µ0A).
For a uniform gap of length g and area A, neglecting fringing, the gap reluctance is Rg = g/(µ0A). In a linear series magnetic circuit with core reluctance Rc, flux is Φ = NI/(Rc + Rg). N is turn count and I is current.
The MathWorks reluctance reference states the constant-reluctance relationship and its geometric variables. This circuit analogy assumes a selected common flux path. It does not independently capture leakage, nonuniform field, hysteresis or saturation, so its simple series sum cannot represent every real assembly.
03 / Field energy
Energy density differs from total stored energy.
For a linear air region, magnetic energy density is u = B²/(2µ0), in J/m³.
For a linear air region, magnetic energy density is u = B²/(2µ0), in J/m³. With uniform B in gap volume Ag, gap energy is Wg = B²Ag/(2µ0). The volume and field magnitude both matter; field energy density alone does not determine the total.
At fixed B and A, increasing g increases this gap-energy expression. Maintaining that same B generally requires a changed excitation condition because gap reluctance also increases. Thus the comparison does not mean that cutting a larger gap into an unchanged current-driven device automatically increases its stored energy.
04 / Fixed excitation
A constant-current comparison has a different trend.
For fixed N and I in the stated linear path, increasing gap reluctance reduces Φ and inductance L = N²/(Rc + Rg).
For fixed N and I in the stated linear path, increasing gap reluctance reduces Φ and inductance L = N²/(Rc + Rg). Total magnetic energy W = ½LI² then decreases. This does not contradict the fixed-B comparison: the controlled variables are different.
Hypothetically, doubling total reluctance at unchanged turns and current halves flux, inductance and total stored energy. That ratio illustration supplies no real gap length, current or component value. It isolates the fixed-excitation condition rather than recommending a physical modification.
05 / Field departures
Gap-edge behaviour differs from a uniform-area assumption.
Near a discrete gap, field lines can spread into surrounding regions.
Near a discrete gap, field lines can spread into surrounding regions. This fringing changes the local field distribution and can interact with nearby conductive structures. Replacing it with one uniform gap area omits those spatial effects, even if the model still captures a broad reluctance trend.
The saturation guide concerns nonlinear material response. A gap and saturation are related through excitation and field distribution, but are not the same phenomenon. A gap-energy calculation alone establishes neither core-loss magnitude nor a saturation margin.
06 / Model boundary
Storage is a state quantity, not an efficiency promise.
An ideal gap stores field energy rather than dissipating it as heat.
An ideal gap stores field energy rather than dissipating it as heat. Real losses can arise elsewhere in the core, conductors and nearby structures, including effects influenced by field distribution. Their calculation requires the corresponding mechanisms rather than treating all stored joules as lost joules.
No gap construction, inductance, core material or operating limit is confirmed for MARSTON equipment by this guide. It supplies no gap alteration, component choice or winding instructions. Its central distinction is whether a comparison holds magnetic state or electrical excitation fixed.
Related technical guides: Generator Flux Linkage and Leakage: Define the Reference · Magnetic Energy and Coenergy: Fixed Variables in Torque · Snubber Concepts: Transient Energy, Peak Voltage and Damping.
General background: Magnetics: Discrete and Distributed Inductor Gaps · MathWorks: Reluctance Geometry and Magnetic Variables. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Gap reluctance | Rg = g/(µ0A) | Uniform air region and negligible fringing. |
| Excitation | NI in ampere-turns | Fixed turn count and current must be identified. |
| Flux | Φ = NI/(Rc + Rg) | Linear common-path series magnetic circuit. |
| Gap energy | B²Ag/(2µ0) in J | Uniform gap field and defined volume. |
| Total energy | ½LI² | Linear zero-biased model with its excitation condition. |
Engineering questions.
Does more gap always mean more stored energy?
No. The answer changes between fixed flux density and fixed ampere-turns.
Is gap energy density the total gap energy?
No. The defined gap volume must also be included.
Does a gap guarantee a core never saturates?
No. Actual excitation and nonlinear material behaviour still matter.
What does fringing add to the picture?
It describes field spreading near gap edges that a uniform-area model omits.
Is energy stored in the gap automatically heat loss?
No. Storage and dissipation are different physical quantities.
Does the reluctance ratio example identify a product inductor?
No. It is a hypothetical linear comparison without actual component values.
Technical enquiry
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