Magnetic Flux Calculator

Magnetic flux: Φ = B·A·cos(θ)

Magnetic flux tells you how much of a magnetic field actually passes through a surface. The formula is Φ = B · A · cos(θ), where B is the magnetic field in tesla (T), A is the area in m², and θ is the angle between B and the normal to the surface. Flux is measured in weber (Wb = T·m²). According to Faraday's law, a flux that changes over time induces an electromotive force, ε = −dΦ/dt. The minus sign comes from Lenz's law, which says the induced current pushes back against whatever is changing the flux. Example: take a 100-turn coil with B = 0.1 T and A = 0.01 m² held perpendicular to the field. Each turn carries Φ = 0.001 Wb, and adding up all 100 turns gives 0.1 Wb of linked flux.

Applications: generators, transformers and MRI

Flux is behind a lot of everyday technology. Electrical generation relies on it (hydroelectric turbines spin coils through a field), as do transformers (where mutual flux couples the primary and secondary windings), electric motors, and MRI scanners (1.5–3 T in the clinic, with research machines reaching 7–11 T). The same principle reads magnetic stripe cards, since the stripe dumps flux under the head, and it makes electric guitar pickups work, where a vibrating string nudges the field across the coil.

FAQ

What happens when θ = 90°? The field runs parallel to the surface, so no field lines cross it and Φ = 0. You get the most flux at θ = 0°, with B perpendicular to the surface.

How does a generator produce voltage? As the coil rotates, θ keeps changing, which makes Φ rise and fall in a sine wave. That changing dΦ/dt is what induces the AC voltage.

What's the difference between flux Φ and flux density B? Think of B as the field packed into each unit of area (T = Wb/m²), while Φ is the grand total over the whole surface. To get Φ, just multiply B by the perpendicular area.

Does flux apply to permanent magnets? It does. Flux shows up any time a magnetic field crosses a surface. What induces voltage is the time derivative dΦ/dt, so a magnet sitting still next to a coil that isn't moving produces no EMF at all.