Physics 9702 · Paper 4

Magnetic Flux & Flux Linkage

Induction is all about how much field passes through a loop — so before any laws, the counting quantity itself, and the two traps hiding in the letter $N$ .

Flux: field through an area

\Phi = BA\cos\theta

Symbols

$\Phi$ = magnetic flux through the area (Wb (weber = T m²))
$B$ = magnetic flux density (T)
$A$ = the area of the loop (m²)
$\theta$ = angle between the field and the normal to the area (—)

Flux counts the field passing through the area. Face-on: Φ = BA. Tilted by θ from the field direction (measured to the normal): only the perpendicular component counts, Φ = BA cos θ — and edge-on the flux is zero.

The definition is two marks: the product of flux density and area, with the area perpendicular to the field — the perpendicular clause is the second mark (9702/42/M/J/23 Q6(a)(i)). One weber is the flux when 1 T passes through 1 m² face-on; exams test it through “give a unit”.
A coil of $N$ turns encloses the flux $N$ times over: the is $N\Phi = BAN$ .

Common mistake

A 2024 question punished the

N

confusion in both directions within two parts: “flux through one turn” means

BA

with no 340, while “flux linkage” two lines later needs the ×340 — the multiplication was a named mark (9702/42/M/J/24 Q7(b)). Read which quantity is asked before touching the calculator.

One more subtlety: the field inside a solenoid is uniform, so a small coil moved along inside it keeps a constant flux linkage — the sketch answer is a flat horizontal line, and “constant flux density” is the explanation mark (9702/42/F/M/24 Q6(a)).

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