Electromagnetism: B-H Hysteresis, Eddy Currents & Core Losses
Why do transformer cores hum, heat up on no-load, and require paper-thin insulated steel laminations? Explore the microscopic physics of magnetic materials: Weiss domain dipole rotation, non-linear B-H hysteresis saturation loops, remanent flux (Br), coercive force (Hc), Steinmetz iron loss calculations, and laminated eddy current suppression under BS EN 60404.
Electromagnetic B-H Hysteresis & Domain Workbench
Magnetizing Force (H) ➔ Microscopic Dipole Spin ➔ Flux Density (B) ➔ Steinmetz Loop LossFirst-Principles Engineering Deep-Dive
Weiss Domain Rotation
Ferromagnetic materials are composed of microscopic magnetic domains (Weiss domains). Without an external field, domains point in random directions, canceling net magnetization. Applying magnetizing force H exerts torque on electron spins, expanding favorably oriented domains until all dipoles align in parallel at magnetic saturation (Bsat).
Steinmetz Core Loss Area
Because domain wall movement is irreversible, flux density B lags behind magnetizing force H, tracing out a closed B-H hysteresis loop. The enclosed area represents thermal energy lost per cycle as heat: Wh = ∮ H dB. Steinmetz's law models this as Ph = η × f × Bmax1.6.
Why Transformers Hum (100Hz)
When iron is magnetized, electron orbital alignment causes tiny physical dimensional changes (magnetostriction) on the order of parts per million. Under 50 Hz AC excitation, the core elongates and contracts twice per cycle, generating the characteristic 100 Hz acoustic transformer hum.
Ferrite vs Laminated Silicon Steel
At 50 Hz, grain-oriented silicon steel is ideal because of its high saturation flux (2.0T). However, at ultrasonic frequencies (100 kHz), its metallic conductivity creates prohibitive eddy losses. Switch-mode supplies therefore use ceramic power ferrites (MnZn) whose electrical resistivity is 1,000,000× higher.
5-Pillar UK Statutory & Standards Compliance Framework
BS EN 60404 Series: Magnetic Materials (Measurement of Magnetic Properties)
Defines standardized Epstein frame and single sheet test methods for measuring specific total loss (W/kg), relative permeability, and magnetic saturation under AC excitation.
BS 7671:2018+A3:2024 Section 521: Electromagnetic Effects in Ferromagnetic Enclosures
Requires that all phase conductors and neutral of an AC circuit enter a steel enclosure through the same knockout hole or slot to prevent induced magnetic eddy currents in the metal casing.
ENA Technical Specification 41-24: Substation Acoustic Noise & Magnetostriction
Specifies permissible sound pressure levels for distribution substations adjacent to residential boundaries, mandating anti-vibration core mounts to isolate 100 Hz magnetostrictive hum.
Control of Electromagnetic Fields at Work Regulations 2016 (CEMFAW)
Transposes EU EMF Directive 2013/35/EU into UK law, setting Exposure Limit Values (ELVs) for workers near high-current magnetic conductors and transformer substations.
BS EN 61000-4-8: Power Frequency Magnetic Field Immunity
Defines immunity testing for industrial electronic equipment exposed to continuous and short-duration 50 Hz stray magnetic fields generated by adjacent heavy switchgear.