UK ELECTRICAL NEWS
Transformers & Magnetics⏱️ 8 min interactive● Live Interactive Simulation

Electromagnetism: B-H Hysteresis, Eddy Currents & Core Losses

Why do transformers hum, warm up on no-load, and require paper-thin insulated steel laminations? Explore the microscopic physics of magnetic circuits: Weiss domain rotation, non-linear B-H hysteresis saturation loops, remanent flux (Br), coercive force (Hc), Steinmetz iron loss calculations, and why laminated core steel reduces destructive circulating eddy currents by up to 99% under BS EN 60404.

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B-H Hysteresis Loop & Domain Alignment Scope

Magnetizing Field (H) ➔ Weiss Domain Spin ➔ Flux Density (B) ➔ Steinmetz Loop Loss
Frequency:
B-H HYSTERESIS LOOP (FLUX DENSITY VS FIELD STRENGTH)B = +1.65 T • H = +450 A/m
Dynamic B-H Trajectory Remanence (B_r = 1.25T) Coercivity (H_c = 45 A/m)
MICROSCOPIC WEISS DOMAIN ATOMIC SPIN ALIGNMENTDomain Alignment: 92% Saturation
Ferromagnetic Atomic Magnetic Dipoles Barkhausen Domain Wall Barking
Peak Flux Density (B_pk)1.68 Tesla
Relative Permeability (μ_r)4,200 μ0
Steinmetz Hysteresis Loss (P_h)0.82 W / kg @ 50Hz
Core Saturation Level84% (Linear Region)

Core Laminations & Eddy Current Losses

Solid Iron Core vs 0.27mm Carlite Laminated Stack • Loss Scaling (d²)

Alternating magnetic flux (Φ) passing through conductive core steel induces internal circular voltages that drive circulating eddy currents. Because eddy current power loss scales with the square of lamination thickness (Pe ∝ f² • B² • d²), splitting a solid 50mm core into insulated 0.27mm steel sheets slashes eddy current heat losses by over 99.9%!

Lamination Thickness & Eddy Current Simulation0.27 mm CRGO (Carlite Insulated)
📏 Steel Sheet Thickness (d):0.27 mm (Modern Transformer Grade)
0.10 mm (Amorphous)0.27 mm (M4 CRGO)0.50 mm (Stator Sheet)2.0 mm (Thick Plate)Solid Block (50 mm)

Eddy Loss Physics & Thermal Impact

Comparing the thermal dissipation of transmitting 1.5 Tesla flux through a 10 kg magnetic steel core at 50 Hz:

Solid Iron Core Loss1,450 W (Core Melts!)
0.50 mm Stator Steel12.8 W
0.27 mm M4 CRGO Steel2.4 W (99.8% Reduction)
Amorphous Metal (0.025mm)0.2 W (Super-Low Loss)
INSULATION STANDARD

Carlite Varnish Insulation: High-efficiency CRGO sheets are coated with a microscopic (1-2 μm) inorganic magnesium phosphate ceramic layer that withstands 800°C stress-relief annealing without breaking electrical isolation.

Magnetic Circuit Ohm's Law & Air Gap Reluctance

MMF (&mathcal;F = N•I) • Reluctance (&mathcal;S) • Magnetic Flux (Φ = &mathcal;F / &mathcal;S)

Just as electromotive force drives current through electrical resistance (I = V / R), magnetomotive force drives magnetic flux through magnetic reluctance (Φ = &mathcal;F / &mathcal;S). Because air has a relative permeability of μr = 1 compared to μr = 4,000 for silicon steel, even a microscopic 1 mm air gap consumes over 85% of the total winding MMF.

C-Core Magnetic Circuit with Adjustable Air GapAIR GAP: 0.50 mm
🪚 Air Gap Length (l_gap):0.50 mm

Live Magnetic Reluctance Balance

Steel Core Reluctance (&mathcal;S_steel):79,500 A/Wb (12% MMF Drop)
Air Gap Reluctance (&mathcal;S_gap):530,000 A/Wb (88% MMF Drop!)
Total Reluctance (&mathcal;S_total):609,500 A/Wb
Total Magnetic Flux (Φ):0.82 mWb (Peak)

Engineering Consequence: In induction motors, the air gap between stator and rotor must be kept ultra-narrow (0.3mm to 1.5mm) solely to prevent excessive magnetizing current from wrecking the motor's power factor.

First-Principles Derivations & Statutory Material Standards

Steinmetz Equations • BS EN 60404-8-7 • Soft vs Hard Magnetics
01

Steinmetz Hysteresis Loss Equation

The power dissipated per kilogram of magnetic core steel during cyclic AC magnetisation is directly proportional to the area enclosed by the B-H hysteresis loop:

Ph = ηst • f • (Bmax)1.6 [W / kg]

Where ηst is the material Steinmetz coefficient (≈ 0.001 for silicon steel, 0.025 for cast iron), f is grid frequency in Hz, and Bmax is peak flux density in Tesla. For B > 1.5 T, the exponent increases from 1.6 to 2.0 due to deep domain saturation.

02

Classical Eddy Current Loss Equation

By integrating Faraday's law of induction around circulating current loops in a rectangular lamination sheet of thickness d and electrical resistivity ρ:

Pe = [ π² • f² • (Bmax)² • d² ] / [ 6 • ρ • D ] [W / kg]

Notice the d² term: halving lamination thickness cuts eddy losses to 25%. Adding 3.2% silicon to electrical steel quadruples electrical resistivity (ρ), further suppressing eddy currents.

03

BS EN 60404-8-7 Grain-Oriented Grades

Under British Standard BS EN 60404, electrical steel is classified by maximum total specific loss at 1.7 Tesla / 50 Hz:

• M080-23N: 0.23 mm thickness, max 0.80 W/kg (Ultra-Premium)
• M097-27N: 0.27 mm thickness, max 0.97 W/kg (UK Tier 2 Grid Standard)
• M130-35S: 0.35 mm thickness, max 1.30 W/kg (Distribution Standard)
04

Soft vs Hard Magnetic Materials

Ferromagnetic materials fall into two distinct engineering classes:

Soft Magnetic Materials (Transformers, Motors, CTs): Narrow B-H loop, ultra-low coercivity (Hc < 50 A/m), high permeability. Easily magnetized and demagnetized with minimal heat loss.

Hard Magnetic Materials (Permanent Magnets, NdFeB): Massive B-H loop, enormous coercivity (Hc > 800 kA/m), high remanence. Resists demagnetization to lock in permanent magnetic flux.
Cross-reference magnetic physics, power transformers, and protection
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3D VISUAL LAB

Transformers: Mutual Induction & Efficiency

See how magnetic flux transfers energy between windings, explore Dyn11 vector groups, and UK EcoDesign Tier 2 loss limits.

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3D VISUAL LAB

Inside an RCD: Toroidal Core Physics

Explore how high-permeability Mumetal cores detect 30mA residual earth fault flux and polarized relay mechanics.

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3D VISUAL LAB

Power Factor & AC Power Triangle

Discover how alternating core magnetization draws non-working reactive kVAR current from the UK grid.

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SIZING ENGINE

Power Converter & Transformer Sizing

Calculate apparent kVA, active kW, full load line currents, and winding I²R thermal dissipation.