Magnetic Flux Converter

Magnetic flux is the total magnetic field passing through a surface, in webers (Wb) in SI or maxwells (Mx) in CGS. A refrigerator magnet produces ~1 mWb through its pole face. Dynamos and generators convert motion to flux changes to induce voltage, a direct consequence of Faraday's law of induction — which is arguably the most commercially important equation in physics, given it underlies every electric motor, generator, transformer, and inductor ever built. 1 Wb = 10⁸ Mx is the fixed ratio; everything else is geometry and turn count.

The weber (Wb) is SI — equivalent to a volt-second — defined so that 1 Wb, changing at 1 Wb/s, induces 1 V in a single loop (Faraday's law: EMF = -dΦ/dt). The maxwell (Mx) is CGS — 1 Wb = 10⁸ Mx. Not to be confused with flux density (tesla or gauss), which is flux per area: 1 T = 1 Wb/m² = 10⁴ G = 10⁸ Mx/m² = 10⁴ Mx/cm². Flux is the integral of field over area; it's what the changing-flux rule acts on, and what transformers, motors, and generators manipulate to convert between mechanical and electrical energy.

For a single loop in a uniform field B perpendicular to the loop area A, flux Φ = B × A. In a multi-turn coil, flux linkage is Φ × N (the 'weber-turns'), which is what sets the coil's inductance (L = NΦ/I). When a generator rotates a coil in a field, flux varies sinusoidally and induces an AC voltage whose amplitude scales with RPM and peak flux — the fundamental scaling that lets hydroelectric dams run at 60 Hz by spinning at 3,600 RPM in a two-pole configuration, or 1,800 RPM for four poles.

Weber to maxwell: multiply by 10⁸. Flux Φ = field × area (for uniform fields). A 0.5 T field through 1 m² is 0.5 Wb = 5 × 10⁷ Mx. Faraday's law: induced voltage V = -N × dΦ/dt, where N is turn count. A transformer with 1 Wb peak flux at 60 Hz in a 100-turn secondary produces V_peak = 100 × 2π × 60 × 1 = 37.7 kV peak. Scale down: 1 mWb peak flux and 100 turns gives 37.7 V peak.

• Weber (Wb)
• Milliweber (mWb)
• Microweber (µWb)
• Maxwell (Mx)
• Kilomaxwell
• Tesla-meter² (T·m²)
• Volt-second (V·s)
• Gauss-cm²

• Flux vs flux density. Flux (Wb, Mx) is total through an area; flux density (T, G) is per area. A 1 T field through a 1 cm² area is 1 × 10⁻⁴ Wb = 100 µWb = 10⁴ Mx.
• Webers per turn vs total flux linkage. In transformer calcs, 'flux linkage' is flux × number of turns (NΦ); easy to mix with raw flux. Datasheets sometimes state flux linkage in Wb-turns.
• Peak vs RMS vs average flux. AC transformer analysis usually quotes peak flux (for core saturation) but RMS voltages. B_peak = V_rms × √2 / (N × 2π × f × A). Getting the √2 wrong under-sizes the core.
• Core saturation. Every core has a saturation flux density (silicon steel ~1.5-2 T; ferrite ~0.3-0.5 T). Exceed it and permeability collapses — inductance drops, current spikes, core heats. Transformer and inductor design is always flux-density-limited at high power.
• Gap and fringing. An air-gapped core increases effective reluctance and stores energy linearly. Flux through the gap can 'fringe' outward, reducing the effective gap area and confusing calculations. Real designs use 3D FEA for precision.

• Refrigerator magnet through pole face: ~1 mWb (100 Mx).
• Small 50-60 Hz transformer primary flux: ~1 mWb peak.
• Medium power transformer (5 kVA, 230 V): ~10 mWb peak at 60 Hz.
• Large power transformer (100 MVA): 1-2 Wb peak over the core area.
• Single turn of a 1 kW microwave oven magnetron transformer: ~5 mWb peak.
• MRI scanner bore (3 T × 0.4 m² opening): ~1.2 Wb.
• Earth's total flux through a 1 m² horizontal loop at mid-latitude: ~25 µWb (2,500 Mx).
• Hard disk drive write-head pole tip (as the head flies): ~1 × 10⁻¹² Wb per bit.
• CERN Large Hadron Collider dipole through beam pipe: ~0.04 Wb.

• Flux = B × A for uniform fields. For non-uniform, integrate: Φ = ∫ B · dA.
• For transformer design, size the core by V = 4.44 × N × B_max × A × f (RMS voltage, 60 Hz sine).
• For motors and generators, flux × turns × rotation rate sets the EMF.
• For sensors (rotary encoders, magnetic switches), changing flux is what triggers output.

Related: Magnetic Field Converter · Inductance Converter · Electric Current Converter.