Faraday’s Law: Flux Linkage

Last time, we saw different ways of inducing an emf in a coil…all of which changed the flux through the coil.

And the greater the rate of change of flux through the coil, the greater the magnitude of the induced emf.

Now, the magnitude of the emf induced in a coil also depends on the number of turns.

Since, if we change the flux through the coil … then we induce an emf in this turn

But we also induce an emf in this turn

…and this turn too!

And in fact, if we change the flux through the coil, we induce an emf ineach turn.

So, to quantify the flux through all the turns…we can take a single turn… calculate the flux through it… and multiply by the number of turns, N. 

And we call this, the flux linkage through the coil.

And, rather than using a different symbol, we normally just write flux linkage as N phi, since it’s the number of turns, multiplied by the flux.

Next, the units of flux linkage are weber turns

Since flux is measured in webers and the number of turns is measured in, well, turns!

And, even though “turns” isn’t really a proper unit, we tend to use it for flux linkage, just to distinguish it from flux.

So now, what’s the flux linkage going through this coil? 

We know the flux through the coil is equal to the flux density multiplied by the area of the coil.

And the area of the coil is this.

Then, the flux linkage is equal to flux multiplied by the number of turns.

So the flux linkage going through this coil is this.

Finally, instead of saying flux linkage, you might see textbooks talk about the amount of flux ‘linking’ a coil.

For example, you could say the flux linking this coil is 0.0026 weber turns… but, generally, we’ll stick to saying ‘flux linkage’.

So, to sum up…

The flux going through a coil multiplied by the number of turns of the coil is called the flux linkage.

And the formula for flux linkage is this. Where this is the number of turns, and this is the flux.