Explain the concept of Flux for me

[Cogman]

the power went out today, so naturally I pulled out the good ole physics book and started going over what ill be studying next semester in college. I ran into the concept of flux being used to describe magnetic fields. Could someone explain the concept of flux, the picture in the book had a plain that was pierced by several arrows and then had another of the plane being bent downward so the arrows pierced it twice.

So what does the plane represent and what do the arrows mean, in their frequency of dotting the plane. Thanks

 

[BrownTown]

http://en.wikipedia.org/wiki/Flux

I mean seriously you are asking for a textbook definition of a word, should take 10 seconds to Google it, 5 seconds to type it into wiki.

 

[Cogman]

Hey, come on I know how to wiki and google, but it is far better to have multiple views from different people on the subject (yes I know that is what the wiki is). Just like I could wiki the string theory or any other theory question and get a good answer, sometimes too good of one. Please, Im going for experiences and analogies here, not a textbook definition (I read the textbook, remember!)

Now anyone else? I don't want just a link to wiki or google, I want what you think it is (or know it is). Im trying to keep the HT area interesting.

One last thing, Why post a question about anything with the mentality that you have just displayed, I mean, most things can be found out with a wiki and google. Would you rather remove all questions from the forum?

 

[esun]

Flux is a measure of the amount of a vector field passing through a surface (defined by an area and a direction). So it's a little different from E fields and B fields (which are vector fields). In physics, usually you deal with simple cases where the vector field is some function and the surface is symmetric to make the calculation easy. More generally, you would have to split the surface into infinitesimal area components (each with an area dA and a direction A hat) and integrate the field over all of those components.

 

[f95toli]

I think Browntowns point is that you can't really have an "opinion" about what flux is. Flux is, by definition, the surface integral of the magnetic field over a given area.
If you want you can think of it as a measure of much field is "contained" by a given area.
If you have a conducting ring with area A in a magnetic field. The flux thorugh the ring is simply
\Phi=B A

If it happens to be a superconducting ring, the flux is quantized. One flux quanta (\Phi_0) is equal to h/2e=2e-15 Wb (h being Planck's constant and e the charge of an electron).
When a superconducting quantum interference device (SQUID) is placed in a magnetic field the supercurrent through the SQUID will (usually) be modulatet with a periodicity \Phi_0.
\Phi_0 is a very small number which is why SQUIDs can be used as very sensitive magnetometers.

 

[esun]

It's pretty clear he wants an explanation relevant to a physics class he'll be taking next semester. Heck, the OP says "Could someone explain the concept of flux", not "what is the definition of flux", which are very different questions.

 

[QuantumPion]

flux: how much it's raining (rain drops per second)
scalar field: how hard its raining (size of drops)
vector field: how fast it's raining (speed & direction of drops)

I haven't thought this through thoroughly so someone tell me if I made a mistake

 

[CycloWizard]

Originally posted by: BrownTown
http://en.wikipedia.org/wiki/Flux

I mean seriously you are asking for a textbook definition of a word, should take 10 seconds to Google it, 5 seconds to type it into wiki.

The Wiki article is incorrect in places, so that's not necessarily a great way to figure out what the real answer is. For example, it says that volumetric flowrate is a flux, but that's incorrect. A volumetric flowrate is actually what I (and most engineers) would call a net transfer rate, which is the integral of a flux over a surface. Of course, this mistake is referenced to an article on groundwater, which was probably written by a civil engineer, so it's little wonder that such a mistake was made.

f95toli gave a good definition of flux in the physicist's sense, while the following is how an engineer would generally define it. Flux describes a relative rate at which some conserved quantity (mass, energy, or momentum) crosses a unit surface. It is an intrinsic quantity that is independent of the material behavior such that no constitutive relationship must be assumed to ascertain the flux using the conservation (Navier-Stokes or simiar) equations. As I said above, to get the net transfer rate of your conserved quantity across your entire surface, you simply integrate the flux over the surface.

If you get more into the nitty-gritty, consider the steady-state diffusion of some chemical A through a barrier. If the barrier is rectangular, then the flux is constant everywhere within the barrier. The mass transfer rate is also constant everywhere within the barrier. If, however, the barrier is cylindrical or spherical, then the flux will vary as 1/r or 1/r^2, respectively, where r is the radial position. However, in these latter cases, the mass transfer rate is again constant at all positions. The flux is highest near the interior of the barrier and decreases as the surface area available for diffusion increases, but the net transfer rate must stay constant everywhere to satisfy conservation of mass.

 

[Modelworks]

flux, the stuff that goes along with solder to make it flow

 

[BrownTown]

Originally posted by: f95toli
I think Browntowns point is that you can't really have an "opinion" about what flux is.

Yes, this is what I am getting at, I'm not really sure when the OP asks for "multiple views" concerning the subject that you can really get that since we are talking about a very rigorously defined term. I know the response comes off harsh and that is my fault I shouldn't have worded it that way, its just imo there are too many threads here about questions that could simply be solved with a little research.

I guess in your diagram the lines are the magnetic field, and the plane is an arbitrary surface through which the lines are flowing. Therefore the magnetic flux would be the integral of the lines through the plane.

 

[wwswimming]

Originally posted by: Cogman
Hey, come on I know how to wiki and google, but it is far better to have multiple views from different people on the subject

it's the way knowledge was passed down in the olden days. like, 1996.

 

[hypn0tik]

Originally posted by: f95toli

I think Browntowns point is that you can't really have an "opinion" about what flux is. Flux is, by definition, the surface integral of the magnetic field over a given area.
If you want you can think of it as a measure of much field is "contained" by a given area.
If you have a conducting ring with area A in a magnetic field. The flux thorugh the ring is simply
\Phi=B A

-Snip-

This is a really good definition. My Gr. 12 physics teacher described it as: FLUX = Field Lines per Unit Area (cross section perhaps?).

 

[Casawi]

Originally posted by: hypn0tik

This is a really good definition. My Gr. 12 physics teacher described it as: FLUX = Field Lines per Unit Area (cross section perhaps?).

I like that.

If you are just taking physics classes then wiki definition is good enough. However it gets little bit hairy in details when you get to EMAG 2 for example. In my case I just walked into my professor's office hours and I asked all conceptual questions I had, and sealed the deal there.

 

[Farmer]

hypn0tik:

That is an intuitive definition, but it is misleading: there are an infinite number of field lines 'going through' any given surface S, given any vector field. I mean, a vector field in itself implies that there is some vector at every point in space (x1, x2, x3, ...). It really has a lot more to do with the magnitude of the vectors in question at the positions in question (i.e., all points on the surface in question). I mean, it's not the quantity through, it's the rate through.

All:

I mean, the easiest way to think of it, if you cannot get it intuitively, is to think in terms of dot products. Let's think in terms of infinitesimals, since that is more general. Suppose you have some "local" surface element dA, which is essentially a plane. To define that plane, we make some vector n s.t. n is unit and perpendicular to the plane. In that local area, there is also a vector, call it b. Then the "flux through dA" is simply b dot n. So it is a vector projection, in the direction of n; i.e., it captures the component of the b in the same direction as n, and returns that magnitude.

When you generalize to the nonlocal case, you just sum all of those b dot ns for all the little bs and all the little dAs. So, you get that flux of some field B through any surface A is integral over A of B dot dA. When the surface is a plane, the integral reduces to finding the area of the plane. When the vector field and surface normal vector are parallel, the dot product reduces to a scalar product.

 

[BrownTown]

Originally posted by: Farmer
I mean, the easiest way to think of it, if you cannot get it intuitively, is to think in terms of dot products. Let's think in terms of infinitesimals, since that is more general. Suppose you have some "local" surface element dA, which is essentially a plane. To define that plane, we make some vector n s.t. n is unit and perpendicular to the plane. In that local area, there is also a vector, call it b. Then the "flux through dA" is simply b dot n. So it is a vector projection, in the direction of n; i.e., it captures the component of the b in the same direction as n, and returns that magnitude.

When you generalize to the nonlocal case, you just sum all of those b dot ns for all the little bs and all the little dAs. So, you get that flux of some field B through any surface A is integral over A of B dot dA. When the surface is a plane, the integral reduces to finding the area of the plane. When the vector field and surface normal vector are parallel, the dot product reduces to a scalar product.

Darn, if thats the easy way to explain it I'd hate to see the hard way. I would say the REAL easy way to explain in would just be "the amount of something going through a surface". Since the OP jsut asked for flux in general and we could be talking about dopant diffusion in semiconductors, induced currents from magnetic fields, the flow of electric current, or even the flow of water (although we might not use the same nomenclature).

 

[Farmer]

Originally posted by: BrownTown

Originally posted by: Farmer
I mean, the easiest way to think of it, if you cannot get it intuitively, is to think in terms of dot products. Let's think in terms of infinitesimals, since that is more general. Suppose you have some "local" surface element dA, which is essentially a plane. To define that plane, we make some vector n s.t. n is unit and perpendicular to the plane. In that local area, there is also a vector, call it b. Then the "flux through dA" is simply b dot n. So it is a vector projection, in the direction of n; i.e., it captures the component of the b in the same direction as n, and returns that magnitude.

When you generalize to the nonlocal case, you just sum all of those b dot ns for all the little bs and all the little dAs. So, you get that flux of some field B through any surface A is integral over A of B dot dA. When the surface is a plane, the integral reduces to finding the area of the plane. When the vector field and surface normal vector are parallel, the dot product reduces to a scalar product.

Darn, if thats the easy way to explain it I'd hate to see the hard way. I would say the REAL easy way to explain in would just be "the amount of something going through a surface". Since the OP jsut asked for flux in general and we could be talking about dopant diffusion in semiconductors, induced currents from magnetic fields, the flow of electric current, or even the flow of water (although we might not use the same nomenclature).

I don't know; if you can't get it intuitively, then that is the mathematical definition.

I guess I can say, a vector goes through a hoop. Multiply that vector by the area of the hoop to get all the vectors going through that hoop, but that is only specific to planes and uniform fields.

 

[hypn0tik]

Originally posted by: Farmer
hypn0tik:

That is an intuitive definition, but it is misleading: there are an infinite number of field lines 'going through' any given surface S, given any vector field. I mean, a vector field in itself implies that there is some vector at every point in space (x1, x2, x3, ...). It really has a lot more to do with the magnitude of the vectors in question at the positions in question (i.e., all points on the surface in question). I mean, it's not the quantity through, it's the rate through.

You are right in the sense that it can be misleading. However, I didn't mean for it to be a definition or anything rigorous at all. It was just to help the OP get a slightly better picture as to what flux is.

 

[BrownTown]

Originally posted by: Farmer

I don't know; if you can't get it intuitively, then that is the mathematical definition.

I guess I can say, a vector goes through a hoop. Multiply that vector by the area of the hoop to get all the vectors going through that hoop, but that is only specific to planes and uniform fields.

Yes, that was probably the simplest mathematical explanation, its just sometimes its better to understand something conceptually and then get into the math later. I know personally I had a materials science class and the teacher tried to explain Fick's laws (having to do with flux incidentally) with a bunch of differential equations and I was totally stumped. The next year in semiconductor fabrication class another teacher explained it in words and It was suddenly so obvious.

 

[Super Nade]

Some very good points were made here. Instead of restating the same thing in a different way, I would suggest that the OP pick up the Feynman lectures in physics. When in doubt ask Feynman (or Landau) was my mantra when I sought a deeper understanding of very basic questions. Buy it, read it and come back and tell me what you thought of the books.