Magnetic Flux

Magnetic flux Φ_B = ∫B·dA — the 'amount' of B threading a surface.

For a uniform B and a flat loop of area A: Φ_B = B·A·cos θ, where θ is the angle between B and the area-normal n̂.

Unit: weber (Wb) = T·m² = V·s. One weber is a flux that, if collapsed in 1 s, induces 1 V in a single loop.

Φ is maximum when B is parallel to n̂ (loop face perpendicular to B); zero when B is in the plane of the loop.

Flux is a SCALAR, but it has a sign that flips with the chosen normal direction. Conventionally the right-hand rule from the loop's positive sense fixes n̂.

Total flux through a closed surface is ZERO (Gauss's law for magnetism — no magnetic monopoles): ∮B·dA = 0.

Without a changing flux, no EMF is induced — even a coil in a huge constant B has zero EMF.