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# thought inducing mag. flux. question. watch

1. Although it's beyond the scope of the course, I've got a question pertaining to magnetic flux.

It's known that moving a current-conducting wire in a uniform magnetic field that is perpendicular to the plane of the wire will induce an potential difference.

Are the conclusions in my thoughts on this result sound and can somebody please expand on these ideas in a 'teacher' fashion?

It's obvious that the wire must be modeled as a line. That is, the theoretical model of a wire must have infinitely small width and hence it's width is negligible. Thus, in calculation, the wire is one dimensional and only has length. Now, remembering it's orientation relative to the flux; if the wire moves in any direction along it's plane, it's known that an EMF is induced. By Faraday's Law, this is due to the rate of change of flux. But it can only change flux if there's variation in the field. This must mean that on some substantially small scale of consideration, there is always variance in a magnetic field. However, due to the fact it's a uniform field, these variations must also be of a uniform pattern. So, flux must come in loads of varying dense streams and isn't indeed an 'atmosphere' of continuous measurement. (Remember that the visual representations of fields were merely a way to convey the concept of field denisty and direction. It was always maintained that the flux was ubiquitous because we assumed that in a uniform field, there was no two points you could put a sufficiently small magnetic material whereby the force exerted on them would vary).

So Is the flux made up of photons or something and does it follow from above?
2. (Original post by hecandothatfromran)
Although it's beyond the scope of the course, I've got a question pertaining to magnetic flux.

It's known that moving 1) a current-conducting wire in a uniform magnetic field that is perpendicular to the 2) plane of the wire will induce an potential difference.

Are the conclusions in my thoughts on this result sound and can somebody please expand on these ideas in a 'teacher' fashion?
Putting on my "teacher" hat.
Logically, if you want to make correct/meaningful conclusions from initial statements, those statements must themselves be correct and clear.

1) Is the wire you refer to a long straight wire or a wire that is wound as a turn in a coil. You haven't said.
2) A straight wire doesn't have a "plane". You refer to the wire moving "along its plane". A coil has a plane. A straight wire doesn't. Do you mean a straight wire moving along its length or perpendicular to its length?
So initially you are not making it clear what, exactly, the experimental setup is here. You need to get this right first.
3. (Original post by Stonebridge)
Putting on my "teacher" hat.
Logically, if you want to make correct/meaningful conclusions from initial statements, those statements must themselves be correct and clear.

1) Is the wire you refer to a long straight wire or a wire that is wound as a turn in a coil. You haven't said.
2) A straight wire doesn't have a "plane". You refer to the wire moving "along its plane". A coil has a plane. A straight wire doesn't. Do you mean a straight wire moving along its length or perpendicular to its length?
So initially you are not making it clear what, exactly, the experimental setup is here. You need to get this right first.

Yeah, sorry 'bout that.
1) A long straight wire
1) The motion of the wire is perpendicular to it's length. So the flux remains perpendicular to the direction of motion throughout.
4. Next part.

Ok, so the long straight wire is moving perpendicular to its length and perpendicular to the field.

(Original post by hecandothatfromran)

... if the wire moves ..., it's known that an EMF is induced.
Correct. The motion is relative to the field.

By Faraday's Law, this is due to the rate of change of flux. But it can only change flux if there's variation in the field.
With "rate of change of flux" you need to specify what flux you are referring to. In the case of a coil, for example, you talk about the flux "linking" the coil. It's not just any flux.
It's also possible to describe the effect using the idea of "cutting flux".
This is often the way when considering a straight wire.
The wire in this case cuts through the lines of magnetic flux. Have you heard of this?
Flux linkage can change even when there is no change in the field itself. For example, if there is a change in orientation or a movement relative to the field. The field itself doesn't need to change.
Faraday's model of a magnetic field being made up of lines of flux enabled the induced emf to be described either in terms of change in flux linkage, or in terms of a conductor cutting through lines of flux. The two are actually equivalent. Both are manifestations of the Lorentz Force, which you read about here
http://hyperphysics.phy-astr.gsu.edu...ic/magfor.html
Any electric charge that moves in a magnetic field experiences a force that is perpendicular to both its direction of movement and the direction of the field. This force is the origin of the emf in the wire and in a coil.
5. This is really confusing me, sorry. So it's nothing to do with the quantity of flux perpendicular to the motion of the wire? It's the fact that the flux perpendicular to the motion of the wire is changing? Please explain further, thank you.
6. (Original post by hecandothatfromran)
This is really confusing me, sorry. So it's nothing to do with the quantity of flux perpendicular to the motion of the wire? It's the fact that the flux perpendicular to the motion of the wire is changing? Please explain further, thank you.
"Quantity of flux" can only relate to the amount of flux contained in (passing through) some defined area. That's what flux density measures. The amount (quantity) of flux passing through an area = BA where B is the flux density and A the area.
Have you studied this?
and also
-the force on a moving charge in a magnetic field F=Bqv (Lorentz Force)

I didn't say the quantity of flux perpendicular to the motion "is changing".
I said the wire is cutting through flux. The field itself isn't changing.

Have you studied "flux cutting" in relation to Faraday's Law? Some teachers don't do this but prefer to talk about the area swept out by the wire as it moves through the field. This then relates back to the idea of flux density and the amount of flux passing through a specified area.

You need to say what you have studied on this topic as it's not possible for me (or anyone) to teach it to you here. Without knowing this it's difficult to explain things in terms of what you already know.
Start by answering my questions in bold and take it from there.
If you are part way through the study of this topic in school I suggest you wait until you have completed the topic as there is a lot more that needs to link in here.
7. (Original post by Stonebridge)
"Quantity of flux" can only relate to the amount of flux contained in (passing through) some defined area. That's what flux density measures. The amount (quantity) of flux passing through an area = BA where B is the flux density and A the area.
Have you studied this?
and also
-the force on a moving charge in a magnetic field F=Bqv (Lorentz Force)

I didn't say the quantity of flux perpendicular to the motion "is changing".
I said the wire is cutting through flux. The field itself isn't changing.

Have you studied "flux cutting" in relation to Faraday's Law? Some teachers don't do this but prefer to talk about the area swept out by the wire as it moves through the field. This then relates back to the idea of flux density and the amount of flux passing through a specified area.

You need to say what you have studied on this topic as it's not possible for me (or anyone) to teach it to you here. Without knowing this it's difficult to explain things in terms of what you already know.
Start by answering my questions in bold and take it from there.
If you are part way through the study of this topic in school I suggest you wait until you have completed the topic as there is a lot more that needs to link in here.
Yep, I have completed the electromagnetic portion of physics, :P. Please can you expand on the area sweeped concept?
8. (Original post by hecandothatfromran)
Yep, I have completed the electromagnetic portion of physics, :P. Please can you expand on the area sweeped concept?
If a wire length L moves (perpendicular to its length) a distance v through a magnetic field the area it sweeps out is Lv (length of wire times perpendicular distance moved)
The magnetic flux in that area is BLv if B is the flux density.
Have you seen the formula E=BLv ?
If you have completed this topic you will know this equation for the emf generated when a wire length moving at speed v cuts through a magnetic field.
v is the distance moved per second. BLv is the flux "cut" per second.
9. Thanks for the swift replies.

I am fully aware of the equations etc... I just want to understand conceptual evidence of why they follow.

The concept of flux cut can only be applied if there is intrinsic variation in flux density at a sufficiently small scale. As this scale of sufficiency is found where we model charge as having negligibly small width compared to a wires length, surely this must mean that flux is the summed flow of unit quantities comparable in size to charge?

So this must mean the A level implied fact that flux is an 'everywhere atmosphere on a continuous scale' is in fact an A level 'myth of ignorance.' It must in fact be the sum of streams of individual quantities which are comparable in size to charge.

Am i doing something stupid or is that sound?
10. Flux is not a stream, it doesn't flow or go anywhere. It's just a name given to the lines drawn in the mathematical model that Faraday invented. You can see that the same lines can be drawn for any vector field such as gravitation or the electric field.
It's a way of visualising (and quantifying) a vector field. There is no suggestion that the lines really exist or that anything is actually flowing along them. They have no width as they are mathematical constructs. It's not the flux you need to be concerned about, it's the actual field. The field is continuous to the same extent that an electric or gravitational field is.
If you want to take the idea of discontinuity further you need to go way beyond A level into quantum theory.
11. Ok, i'm very confused. I've just found out that a magnetic field is made up of photons. This must surely fit the hypothesis that on a sufficiently scale, (I.E. on a scale pertaining to charge) the common field model is inapplicable on a sufficiently scale. right..?

For the reasons listed below, I just don't understand how flux cutting can apply if the field is truly continuous and/or not motive.

if a square coil of a single turn (so as to under-complicate with another dimension) is placed with it's plane perpendicular to a field it will experience a flux linkage. Now, assuming that the coil is in a uniform field throughout , if it moves in any direction along it's plane, it will not experience an EMF (well known) as there's no rate of change of flux. Now, as one of the dimensions of the plane of the coil converges to 0, the coil may be modeled as a line wire. We know that if the wire were to undergo the same motion it will experience an EMF. So surely there must be a modeling assumption that becomes invalid in the field. I.E, it's not continuous.....

If i'm wrong please specify how, thanks....
12. (Original post by hecandothatfromran)
if a square coil of a single turn (so as to under-complicate with another dimension) is placed with it's plane perpendicular to a field it will experience a flux linkage.
correct

Now, assuming that the coil is in a uniform field throughout , if it moves in any direction along it's plane, it will not experience an EMF (well known) as there's no rate of change of flux.
Correct. (Insofar as) There is no change in flux linking the coil as it moves. There will be no overall emf or current in the coil.

However. The two opposite sides of the coil that are cutting flux experience an emf. (There is the Lorentz force F=BLv on them). Left and right side in first diagram below. These emfs oppose each other in the coil circuit.

Now, as one of the dimensions of the plane of the coil converges to 0, the coil may be modeled as a line wire. We know that if the wire were to undergo the same motion it will experience an EMF.
Correct.
Any conductor in that orientation will experience this emf.
So surely there must be a modeling assumption that becomes invalid in the field. I.E, it's not continuous.....
No. There is no inconsistency in this. In fact it demonstrates the equivalence of flux cutting and change in flux linkage.

Look at this diagram.
Square coil moving to the right. Magnetic field into the page.
Emf induced in the opposite wires as shown in first figure. Check this using the Right Hand Rule.
Second figure. Same idea but coil shrinking.
Third figure. Coil has become a single wire. There is an emf induced in the single wire in the same direction.

There is no contradiction or invalid modelling assumption here.
In the coil the emfs induced by the wires cutting flux are equal and opposite. (Opposite in the sense of clockwise and anticlockwise in the loop.) This results in there being a resultant emf of zero in the coil as predicted by the flux linkage model.

The flux cutting model predicts the same outcome.

I think the only thing which is possibly not explained when this is taught is that in the case of the coil, we are talking about no emf in the loop. That is to say, no induced current flows in the coil. What you can say is that there is an emf across the coil from top to bottom in the same way as there is across the single wire.
However, this emf is not of interest from the point of view of inducing a current in the coil. When talking about emfs in the coil, it means in the electrical circuit/loop.

I hope this has cleared up the misunderstanding.
13. Ah..... Thank you very much. I certainly had a no idea that it was the resultant EMF that was induced in a coil.

However, sorry about this, but i'm still having trouble understanding the concept of flux cutting and flux linkage models. I'm just thinking flux isn't technically cut (because it's a continuous atmosphere) and/or flux cutting can't affect that rate of change of flux linkage (as it cuts flux, it 'exists an equal amount of flux).
14. (Original post by hecandothatfromran)
Ah..... Thank you very much. I certainly had a no idea that it was the resultant EMF that was induced in a coil.

However, sorry about this, but i'm still having trouble understanding the concept of flux cutting and flux linkage models. I'm just thinking flux isn't technically cut (because it's a continuous atmosphere) and/or flux cutting can't affect that rate of change of flux linkage (as it cuts flux, it 'exists an equal amount of flux).
As I've said in previous posts, there is actually no such (physical) thing as flux. Just a field exists.
The idea of flux is a model to help quantify and visualise what's going on.
What does exist is a magnetic force (field). This force has direction and the direction can be represented as lines of flux. It's an experimental fact that if you move a wire or coil in the ways discussed above relative to the direction of the magnetic field, an emf is induced. The lines of flux are there simply to help you picture the magnetic field. You are taking the model/analogy too literally. The imaginary lines of flux certainly are cut. After all, we've invented them. The reality is that you are moving electrons (in the conducting wires) in a magnetic field and these electrons experience a force as a result.
You have to appreciate that when Faraday studied this at the beginning of the 1800s the electron had not been discovered. He had no idea of the actual mechanism of what was going on. There was no explanation. All he knew was that emfs and current were induced when wires and magnets were moved in certain ways relative to each other. He invented the ideas of flux/linkage/cutting etc to create a model.
I really don't get why you are agonising over whether flux really is cut or not. It's just a model. In the model, flux IS cut. In the model, flux links coils and flux linkage changes.
If you move wire parallel (along) the lines of flux (that is, in the same direction as the field) there is no emf induced. This is an experimental fact. If you move it perpendicular to the field an emf IS induced. The idea of the wire not cutting flux in the first example and cutting it in the second is a convenient way of visualising this. There is nothing to be gained by saying that "technically" flux isn't cut in the second case. What does that mean?
If you invent lines of flux and say they are pointing, say, East-West, then if you move East -West you don't cross them or cut them, if you move North South you do. That is an indisputable fact.
The fact that lines of flux are cut when you move across them is as true as the fact that you cross lines of latitude when you travel North or South. Of course the lines of latitude don't actually exist, but they are a very useful idea.

If you want a further example of how flux cutting and flux linkage are just two ways of thinking about the same thing, and how the idea of inventing lines of flux is useful for quantifying magnetic fields, then look at this.

The coil on the left has moved its position to the right.
Using the idea of flux linkage, the amount of flux has changed (increased) as a result. If this took place in one second then that would be the rate of change of flux and we could calculate the emf from Faraday's Law.
If we think of the field as consisting of lines of flux, and the amount of flux as being the number of lines, then we can see that the number of lines linking the coil has increased by 2 as a result of the move.
You can also say that the circumference of the coil has, in the process, cut through 2 lines of flux. The two ideas are equivalent.

Both models give you a way of quantifying/visualising what's happening.
I stress again. This is a model. It's useful insofar as any model is useful.
The reality is that the magnetic field nearer the magnet is stronger than it is further away. Moving the coil has brought it into a stronger field. The closeness of the lines of flux to each other (flux density) can easily be visualised this way and thought of as representing the strength of the field. (Same as electric and gravitational fields)
And the actual mechanism (unknown to Faraday at the time) was the fact that electrons in the wire of the coil as it moves have a velocity that has a component perpendicular to the direction of the magnetic field and experience a force.

I fear we are starting to go round in circles with this and I am starting to repeat myself. I suggest you
-go back and read my previous posts again
-look up Lorentz Force and the force on an electron in a magnetic field
15. Thank you very much for your investing your time and knowledge into helping me understand this. I'm impressed and I truly appreciate it.

I think i'm out of the tunnel on this one, thanks. So, basically my ideas are only applicable to the model. However, what i couldn't understand was that the model is only analogous to the reality of flux and was not a literal conceptual representation of flux (I.E. it's a physics model)?
16. (Original post by hecandothatfromran)
Thank you very much for your investing your time and knowledge into helping me understand this. I'm impressed and I truly appreciate it.

I think i'm out of the tunnel on this one, thanks. So, basically my ideas are only applicable to the model. However, what i couldn't understand was that the model is only analogous to the reality of flux and was not a literal conceptual representation of flux (I.E. it's a physics model)?
Yes, it's just a mathematical (physics) model that attempts to express a reality. It's a way of trying to picture and quantify something that is invisible.

It's actually quite remarkable what Faraday did in his time to come to the conclusions he did. That's why it would be worth reading up on his work.

Give this topic a bit of time to sink in. It can be very tricky and, judging by comments I frequently see on here and the number of requests for help doing questions on flux, one of the hardest parts of the A Level spec. When you next have to do questions on this topic come back and ask for help. (If you need it.)
Good luck.
17. Thank you very much. I truly appreciate it. The inquisition literally kept me up at night. I hope i have more questions to ask you soon!

Thanks again!

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