Magnetic Flux Linkage | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Magnetic Flux Linkage

Magnetic flux describes one turn. A coil has many turns, so the flux through each turn contributes to the whole coil.

One turn becomes many turns

N\Phi=N B A\cos\theta

Symbols

$N\Phi$ = magnetic flux linkage (Wb)
$N$ = number of turns (—)
$\Phi$ = magnetic flux through one turn (Wb)

At fixed flux through each turn, doubling the number of turns doubles the flux linkage.
“Flux through one turn” does not include $N$ . “Flux linkage of the coil” does include $N$ .

Worked example

One turn or the whole coil?

A 340-turn coil has area $3.2\times10^{-4}\ \mathrm{m^2}$ in a field of 7.2 mT. Find the flux through one turn, then the flux linkage (9702/42/M/J/24 Q7(b)).

Find the flux through one turn.
$\Phi=BA$
$\Phi=2.3\times10^{-6}\ \mathrm{Wb}$
Multiply by the number of turns.
$N\Phi=340(2.3\times10^{-6})$
$N\Phi=7.8\times10^{-4}\ \mathrm{Wb}$

Answer

\Phi=2.3\times10^{-6}\ \mathrm{Wb}

N\Phi=7.8\times10^{-4}\ \mathrm{Wb}

Your turnrelationship check

The flux through each turn remains fixed and the number of turns is tripled. State the change in magnetic flux linkage.

Show worked answer

The magnetic flux linkage triples because it is equal to NΦ.