Magnetic Flux
Φ = B·A·cosθ. Tilt the loop and watch flux follow a cosine curve.
Key Notes
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.
Formulas
Magnetic flux (general)
Surface integral over any open surface bounded by the loop.
Uniform field, flat loop
θ between B and the area-vector n̂.
N-turn coil linkage
Each turn contributes; total 'flux linkage' is N times the flux through one turn.
Gauss's law for B
No magnetic monopoles — equal incoming and outgoing field-line counts.
Important Points
Φ is the 'fuel' for induction — and only its CHANGE creates an EMF.
If you rotate the loop in a uniform B, Φ varies sinusoidally with the rotation angle — the basis of AC generators.
Two coils linked by flux are mutually inductive — even without electrical contact.
A solenoid produces uniform B inside, so the flux through any cross-section is B·A — independent of position along the axis.
The 'weber' is the SI unit that closes the V·s connection: dΦ/dt = ε implies Wb/s = V.
For a tilted loop in a uniform field, only the COMPONENT of B perpendicular to the loop face contributes — that's where cos θ comes from.
Magnetic Flux notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.