In my revision guide it says, "flux linking is when emf is induced by changing the magnitude or direction of the magnetic flux."

I'm slightly confused here because earlier on the page it defines "flux linkage" as the total flux times the number of turns on a solenoid (so "flux linking" and "flux linkage" are different?), and in another book it defines "flux linking" as when magnetic field lines pass through an area (e.g. the cross-section of a coil) so the area is "linked" by the flux.

In other words, doesn't flux linking just mean when a magnetic field is passing through an area?

If someone can clarify how these three definitions are related, or if any of them are wrong, I would really appreciate it. My main concern is to know what flux linkage means in "real" physics because I am aware that revision guides tend to dumb down concepts a bit.

Thanks

So many ways to be confused... I will try to tell you how I think about these things.

When I have a coil (one turn, N turns...), and I try to change the magnetic field through the area that the coil surrounds, then I have to have lines of B field "cross" the wires into the area. This may not be a scientifically accurate way to think of it, but it's very helpful for your intuition - because a B line crossing the wire is a bit like the charges inside the wire having a velocity relative to the B field, and it results in a force on the charge and therefore EMF. The more turns I have, the more charge feels the force, therefore the greater the EMF. Similarly, the larger the area, the more B lines have to cross the wire to fill the area with a certain density of lines - again, emf scales with area (or total flux).

So far so good - this is just an intuitive way to think about induction.

Now we add "flux linking". In general, if "flux in A" $\implies$ "flux in B", then we say the two are "linked" (and incidentally, it always means the reverse is also true by something call reciprocity: that is, flux in B will then always imply flux in A). The amount (strength) of the relationship is the linkage. That is,

# linking = there is a relationship between $\phi_A$ and $\phi_b$linkage = how much linking there is

I hope this confused you less, not more, than your revision guide.

• Thank you! Currently posting questions so will read this (and any other reply) as soon as I finish – user45220 May 5 '15 at 18:59