# Flux cutting and flux linking?

I am a bit confused about the difference between flux cutting and flux linking when talking about magnetic fields and induced EMF.

I was originally under the impression that flux cutting was when there was relative motion between a conductor and a magnet and linking was when there was a change in the magnetic flux density.

After reading, it seems that flux linking is when a magnet is moving and a conductor is still whilst flux cutting is the other away round. This makes no sense to me as depending on the reference frame either could be happening so they seem to be indicating the same thing. If this is however the case what do we call it when the magnetic flux density is changing and there is no relative motion?? (a definition of both would be helpful)

Extra: On reading the answers given I think I understand, but just to make sure, would these staments be correct:

1. When a magnet falls through a long metal tube, the field lines of the magnet cut the tube. This is flux cutting.

2. When the flux of the primary coil in a transformer changes, the flux linked with the secondary coil changes. This is flux linking.

3. A metal conductor moves through the magntic field of a magnet and cuts its field lines. Flux cutting.

4. An AC-generator coil spins in a magnetic field, changing the magnetic flux through the coil. Flux cutting or flux linking??

(A bit unrelated but in the expression: $$Flux=BA$$ Is $A$ the cross sectional area of the solenoid?)

• Are they not the same? When a wire "cuts" through a flux, it is linked to it, right? Commented Jun 5, 2014 at 11:56
• Good research done... :-) Commented Oct 26, 2017 at 4:44

Yes, flux cutting and flux linking are different. There are two basic ways of producing an induced emf:

• flux cutting (conductor moves, flux density B remains constant)

As the coil rotates anticlockwise around the central axis which is perpendicular to the magnetic field, the wire loop cuts the lines of magnetic force set up between the north and south poles at different angles as the loop rotates.

Image and description credits: ElectronicTutorials

• flux linking (conductor stays still, B changes.)

When the magnetic flux linking the coil changes, an emf is induced in a coil or conductor.
Image and description credits: 4Mechtech

Credits: Revise A2 Physics for AQA A- Page No.44.

• what is it called when the magnet moves or the flux changes direction?? thanks
– user43487
Commented Jun 7, 2014 at 17:40
• When magnet moves inside the stationary coil as shown above, it is called flux linkage. Commented Jun 7, 2014 at 18:05
• It seems that, same situation may be seen differently by different observers. Commented Jun 7, 2014 at 18:20

The flux encompassed by a coil is the integral of B over area:

$$\Phi = \int \vec{B}\cdot d\vec{A}$$

You can see from this expression that you can change the flux either by changing the area, or by changing the value of B, or the angle between them.

When we talk of flux cutting, we usually mean "the dot product of the area and the B field is changed because their geometric relationship changed". For example, if I move a loop into the opening of a C shaped magnet, I "cut" through lines of B and see a sudden flux in my loop.

On the other hand, if my loop is already inside the C magnet and I rotate it, once again I change the dot product of area and B (this time by changing the angle).

Finally, if I hold the loop still and change the field of the magnet, I change the flux because the value of $B$ changes. In that case, the geometry didn't change, and we speak of flux linking.

The following excerpt from an online A-level physics course shows this in a diagram:

UPDATE

You gave four cases to test your understanding. You were right on the first three; case 4 is flux cutting (the geometry changes).

As for your "unrelated question": in the expression $$Flux=B A$$ $A$ is the area of the solenoid normal to the B field - so if you have a homogeneous B field at an angle $\theta$ to a plane coil, $$Flux = B A cos\theta$$ because that is how you would count "the number of flux lines going through the area of the coil". Put differently, this is how you can see that flux changes when a coil rotates in a magnetic field. It's not that the area of the coil changes, but the "area that sees the magnetic field" changes. This is what the $cos\theta$ term is telling us - and why the integral expression is really the right way to look at this (but that may be a bit more advanced than you need right now).

I hope this clears up the difference. Feel free to ask for further clarification in the comments!