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Permanent Magnet
Neodymium Magnet Flux & Force Air Gap Simulator
Design magnetic circuits using neodymium (N42/N52/N35SH) or ferrite magnets. Adjust magnet size, air gap, temperature, back-iron yoke and Halbach arrangement to see air-gap flux density B and pull force F update in real time, and optimize magnetic holders, sensors and linear motor circuits.
Parameters
Magnet grade
Sets residual flux Br and temperature coefficient
Magnet width
mm
Magnet thickness
mm
Air gap
mm
Distance between magnet face and target steel
Arrangement
Layout boost on the air-gap flux
Ambient temperature
°C
Air-gap shim
cm
Extra non-magnetic spacer (plastic, paper, etc.)
Back-iron yoke
Return-path material for the flux
Results
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Residual flux Br (T)
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Air-gap flux density B (T)
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Pole area (cm²)
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Pull force (kg)
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Magnet volume (cm³)
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Energy density (kJ/m³)
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Magnetic Circuit Visualizer — magnet, yoke, gap, flux lines
Magnet (red/blue = N/S pole) → air gap → steel plate. Curves are flux lines; the arrow shows pull force on the plate.
Air-gap flux density B_gap and temperature-corrected residual flux Br. t: magnet thickness, g: air gap, k_arr: arrangement factor, α_Br: temperature coefficient (−0.12 %/°C for NdFeB).
Pull force F (from Maxwell stress) and magnetic energy density u. A: pole face area, μ₀ = 4π×10⁻⁷ H/m, k_yoke: yoke efficiency (iron 1.5, alnico 1.3, none 1.0).
Neodymium Permanent Magnet — Air-Gap Flux & Force Optimization
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Neodymium magnets are insanely strong. On Amazon I see "N52" and "N42" labels — what do those numbers actually mean?
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Great question. The number is the maximum energy product (BH)_max in mega-gauss-oersted (MGOe). Roughly speaking it's the maximum energy stored per cm³ of magnet. N42 ≈ 42 MGOe, N52 ≈ 52 MGOe, so N52 stores about 24% more energy. In practice we compare them by residual flux Br: N42 ≈ 1.30 T, N52 ≈ 1.45 T. Flip the grade selector on the left and watch the air-gap flux B change.
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I went from 2 mm to 5 mm air gap and the pull force dropped by more than half. Why is the effect so violent?
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Magnetic pull force scales with B², via Maxwell stress: F = B²·A/(2μ₀). And B itself depends on the ratio t/g of magnet thickness to gap, so doubling g cuts B roughly in half and F by about 4×. That's why magnetic holders, sensors and motors always try to "squeeze the gap." A coating that goes from 0.5 mm to 1 mm can shave 20% off the pull force.
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Raising the temperature from 25 °C to 100 °C also drops the force a lot. Is that just NdFeB physics?
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Temperature is NdFeB's biggest weakness. Br has a coefficient of −0.12 %/°C, so a 75 °C rise costs about 9 % of Br and (since F ∝ B²) about 17 % of force. Above the rated temperature, some grades suffer irreversible demagnetization. That's why automotive and industrial motors use Dy-doped grades like N35SH or N42H — usable up to roughly 150–180 °C. Ferrite is even more temperature-sensitive at −0.2 %/°C but costs 10× less.
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Switching to "Halbach" jumped the force by ~1.4× with the same magnet mass. Isn't that cheating?
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It's not cheating — it's clever. Klaus Halbach invented this layout in 1980 for particle accelerators. By rotating each segment's magnetization by 90°, flux is concentrated on one face and almost cancelled on the other. You'll find it in toothbrush vibration motors, linear motor stages, robotic-arm actuators, MRI permanent magnets, and yes, the AirPods Pro case lid. Cost and assembly precision are higher, but per unit magnet mass it's the strongest layout.
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Changing the yoke to "Stainless" dropped the force from 47 kg to 25 kg. Isn't stainless steel non-magnetic?
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"Stainless" depends on the grade. Austenitic SUS304 and SUS316 are essentially non-magnetic (μ_r ≈ 1), so they don't form a return path — flux leaks and the gap field drops. Ferritic SUS430, on the other hand, behaves a lot like pure iron. So "stainless = non-magnetic" is a myth; always check the grade. Magnetic-circuit design boils down to "flux takes the path of lowest reluctance," so design the geometry so leakage paths are far worse than your wanted path.
Frequently Asked Questions
A simple magnetic-circuit model uses the ratio of magnet thickness t and air gap g: B_gap = Br·(t/g)/((t/g)+1)·k, where Br is the residual flux density (about 1.30 T for N42, 1.45 T for N52) and k is an arrangement factor (1.4 for Halbach, 1.5 for two-pole). A smaller gap g brings B closer to Br, while a large g causes a rapid drop. This tool uses that closed-form model and adds temperature and yoke corrections.
Residual flux Br of an NdFeB magnet drops by roughly −0.12%/°C. An N42 magnet at 1.30 T (25°C) falls to about 1.21 T at 80°C and 1.15 T at 120°C. Above its rated temperature, irreversible demagnetization can occur — the limit is about 80°C for N42 and 150°C for N35SH. The tool applies this coefficient so you can see the design margin. Ferrite has a stronger temperature coefficient of −0.2%/°C and changes much more with temperature.
A Halbach array rotates the magnetization 90° from segment to segment, concentrating the flux on one face while nearly cancelling it on the other. This tool models a 1.4× boost over single-pole — used widely in linear motors and MRI permanent-magnet segments. A two-pole attract arrangement (steel plate between opposing magnets) gives about 1.5×. Halbach has cost and assembly tolerance challenges but is the most efficient layout per unit magnet mass.
A yoke provides a return path for the flux, reducing leakage and raising air-gap flux density by 30–70%. This tool uses 1.5× for an iron yoke, 1.3× for alnico, 0.8× for stainless (austenitic grades are non-magnetic), and 1.0× without a yoke. Pure iron or electrical steel gives the best effect, while non-magnetic SUS304 actually weakens the flux by adding reluctance. Always remember: flux follows the path of least magnetic reluctance.
Real-World Applications
Permanent-magnet holders and magnetic chucks: magnetic chucks for machining, industrial magnetic lifters, and even kitchen knife strips all rely on neodymium magnets. Maximum pull force scales with pole area and B², so for holding thin sheets or curved parts a two-pole or yoked design beats a single pole. Industrial lifters that handle steel plates over 500 kg combine N42-grade magnets with pure-iron yokes.
Linear motors and servo motors: maglev trains, CNC servo axes, and robotic arm actuators use Halbach-arrayed magnet segments to produce strong flux while pushing current through coils for thrust. The Halbach boost lets you cut magnet mass by ~30 % while keeping the same force.
Magnetic sensors and rotation pickups: automotive crankshaft position sensors, ABS wheel-speed sensors and industrial encoders combine a magnet on the moving part with a Hall or GMR sensor on the housing. Since sensitivity scales with flux density, choose temperature-stable grades like N35SH so Br stays reliable across −40 °C to 150 °C.
Magnetic toys and education kits: spherical "buckyball" magnets and educational kits store several kg of pull force in a tiny package. That makes accidental ingestion by children a serious hazard, and US CPSC has restricted small high-strength magnets in toys since 2012. Visualizing pull force here helps designers and educators appreciate just how strong these magnets are.
Common Pitfalls and Notes
The biggest trap is "picking a magnet by Br alone." N52 has 12 % more Br than N42, but the operating point of a real circuit depends on both Br and intrinsic coercivity Hcj. In circuits with a wide gap or strong demagnetizing field, a high-Br / lower-Hcj grade like N52 can actually demagnetize and end up weaker than N42. Rule of thumb: if the operating point sits above 70 % of Br, choose N52; below 50 %, prefer N42 or N35SH. This tool ignores demagnetization, so verify production designs with FEM (Ansys Maxwell, JMAG, FEMM).
Second, forgetting temperature correction. Br drops by about −0.12 %/°C reversibly, but exceeding the rated temperature (80 °C for N42, 100 °C for N50M, 150 °C for N35SH) causes permanent loss that persists after cooling. Engine compartments (85–125 °C), solder-reflow ovens (260 °C), and UV-cure ovens are common danger zones. As a safety margin, pick a grade rated 20–30 °C above your worst case.
Third, ignoring leakage flux. This simple model assumes flux only flows straight through the gap, but 20–50 % of the real flux escapes through the sides of the magnet. When the gap is larger than the magnet thickness (g > t), leakage dominates and this model overestimates B. Yokes cut leakage, but once the yoke saturates (pure iron ~2.1 T, SS400 ~1.6 T) excess flux leaks out again. Always validate with FEM and add Mu-metal / Permalloy shields when stray fields are a problem.
How to Use
Select magnet grade (N42, N52, or N35SH neodymium; or ferrite) from the material dropdown—N52 delivers ~1.43 T residual flux but loses 0.11%/°C, while N35SH maintains stability above 100°C.
Input magnet dimensions: width (mm) and thickness (mm). A typical 10×5 mm N52 disc has 0.5 cm³ volume and ~4.2 kJ/m³ energy density.
Set air gap (mm) between pole faces—flux density decreases nonlinearly; 2 mm gap reduces B by ~30% compared to contact, affecting pull force proportionally.
Enter ambient temperature (°C); neodymium grades degrade performance as temperature rises, with pull force dropping to 80% at 80°C for standard grades.
Read outputs: residual flux Br, air-gap flux density B (Tesla), pole area, pull force (kilogram-force), volume, and energy density instantly recalculate.
Worked Example
Design a holding magnet for a 15 kg industrial jig at 22°C. Use N52 grade, 15 mm width, 8 mm thickness, 0.5 mm air gap (typical ferrous plate contact). Calculated pole area: 2.25 cm². Residual flux Br: 1.43 T. Air-gap flux density B: ~1.38 T (slight reluctance loss). Pull force output: 18.2 kg-force—exceeds requirement with safety margin. Increase air gap to 2 mm: B drops to 1.12 T, pull force reduces to 14.8 kg-force, now marginal. Solution: switch to N52 with 12 mm width instead, maintaining 0.5 mm gap to achieve 22.1 kg-force.
Practical Notes
Temperature derating: N42 at 60°C loses 8% pull force; specify N35SH (120°C Curie stability) for furnace-side assemblies or outdoor vibration applications.
Air gap nonlinearity dominates design—halving gap from 3 mm to 1.5 mm increases force by ~40%, not 100%; reluctance grows exponentially at gaps >5 mm.
Ferrite magnets (0.38 T Br) require 6× larger pole area than N52 for equivalent force but cost 70% less and tolerate 250°C without degradation—trade size for thermal robustness in motor commutators.
Volume efficiency: N52 at 4.3 kJ/m³ versus ferrite at 0.8 kJ/m³ means neodymium wins compactness; verify mechanical stress limits (material brittleness) when simulating thick discs >10 mm.