# I am very confused about the physical meaning of the concept flux

1. Mar 26, 2013

### la6ki

I am very confused about the physical meaning of the concept "flux"

I am really trying to understand what it means, what unit it has, but I keep reading contradicting definitions.

So, on the one hand, I read that "...flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity]·[time]−1·[area]−1" (this is from the Wiki article). So basically it is:

Whatever-Quantity/Unit-Area

But then I keep reading and I see that it's actually the surface integral of a vector field. So now we are multiplying the quantity by unit area! So which one is it, are we dividing or multiplying?

Then there is also the notion of flux density... Which is flux per unit area. Well, if the first definition is true, then this becomes [quantity]·[area]−1·[area]−1 or [quantity]·[area]−2. If it's the second definition it becomes [quantity]·[area]−1·[area] or just [quantity]?

Please somebody help me sort the mess that's in my head (or potentially in the terminology itself).

2. Mar 26, 2013

### Kamper

The definitions do not contradict. When you take the surface integral you basicly sum-up all the vectors "flowing" through the surface so both your definitions are the same.

3. Mar 26, 2013

### la6ki

But you multiply the value of your vector field by the unit of surface area, not divide. One definition says:

Flux = F/A

the other definition says:

Flux = FdA

How can they be the same thing?

4. Mar 26, 2013

### Kamper

When evaluating the flux of the vector field you take the dot product of the surface normal to dA and the vector field. So the flux becomes F=V dot NdA

Where NdA is determined by which surface you are evaluating

5. Mar 26, 2013

### la6ki

But when I hear the expression "per unit area" I imagine we are dividing by the area, not taking the dot product. Am I wrong?

6. Mar 26, 2013

### engnr_arsalan

let "B" be the magnetic field a vector quantity passing through area A. now if say ∅= B/A then ∅ represents flux that is magnetic field over an area..and here B can also be called Flux Density which tells how much lines of magnetic lines of force are passing.
the quantity we calculate from surface integral is Flux Density..
i hope this clear some fog in ur mind..thnx

7. Mar 26, 2013

### la6ki

8. Mar 26, 2013

### Staff: Mentor

There is a reason why all this is so confusing. In some practical disciplines, the word flux is used to represent the flow rate per unit area. In other disciplines, the word flux is used to represent the the flow rate over the entire area. So there are actually two conflicting definitions of flux, depending on which area you are working in. To make matters worse, people working in each discipline are unaware that people working in the other discipline use a different definition of flux.

In heat transfer, the heat flux is always the flow rate of heat per unit area, and the typical units are W/m2. In electromagnetics, the flux is always the integral over the entire area, and the units don't have m2 in the denominator.

9. Mar 26, 2013

### xAxis

That's because magnetic field, B is flux density, the nimber of magnetic force lines per unit area. In this case, flux is simply the number of magnetic line forces perpendicular to an area.

10. Mar 26, 2013

### BruceW

yeah, different people will define flux in different ways. This means you need to know what definition someone is using when they are talking to you about flux. Another example, to add to those already mentioned, is for the flow of mass per time:
$$\int \rho \vec{v} \cdot d \vec{S}$$
Now, some people would call the whole integral 'flux', so in this definition, flux would be flow of mass per time. Other people would say that the flux is:
$$\rho \vec{v}$$
In this case, flux is the rate of flow of mass per time (and per area). Probably this second definition is more common in the case of flow of matter. But, as you know, the first definition is also frequently used (for example, in electrodynamics). So you can sometimes guess which definition is being used, but if you can, then check explicitly, which definition someone is using.