Magnetic flux through a flat loop is Φ= BA cosθ, where θ is between B and the surface normal. Flux is largest when the field is perpendicular to the loop and zero when it lies in the loop’s plane. The unit is the weber, Wb=Tm2. For N identical turns, flux linkage is NΦ . The chosen normal defines the sign of flux.
Faraday’s law gives average emf ϵ=−ΔtNΔΦ, or the instantaneous negative gradient of flux linkage against time. Change can come from B, area or orientation. A large steady flux gives no emf if it does not change. For a straight length L moving perpendicular to itself and a uniform B, with motion also perpendicular to B, the motional-emf magnitude is BLv.
Example 1
A 0.0200m2 loop is perpendicular to a 0.300T field. Find flux.
The field is parallel to the area normal, so Φ=BA=0.300×0.0200=0.00600 Wb.
Example 2
A 200−turn coil changes flux per turn from 0.00400 to 0.00100 Wb in 0.100s. Find average emf magnitude.
∣ϵ∣=ΔtN∣ΔΦ∣=200×0.1000.00300=6.00V.
Watch out: Emf requires changing flux linkage; a steady flux gives zero induced emf.