# The Unit of Electric Flux?

1. Oct 28, 2009

### wfunction

Hi all,

What is the unit of electric flux? I know this is an easy question, but I've seen different units.
In the following, I use the integral form of Gauss's law: $$\oint E\cdot dA=\frac{Q}{\epsilon_0}$$

1. Many physics book and parts of Wikipedia vaguely say that the integral on the left side represents the "electric flux", and thus it has units of "electric field" or "electric flux density" (V/m) multiplied by units of area (m^2), which results in "V-m". No problem.

2. When I look deeper, I see that this is apparently incorrect: E is the "electric field strength" while $$\epsilon_0\times E=D$$ is the "electric flux density"; hence, "electric flux density" has units of Coulombs/meter^2.

Personally, I like the latter explanation, but which one is officially correct?
If it's the first one, then is the second one wrong?
If it's the second one, then why is it so hard to specifically find a website that gives the units of electric flux instead of flux density?

Thanks!

2. Oct 29, 2009

### Lev

Let's compare electric field with magnetic field. While we talk about magnetic field, we have a unit B, called "magnetic induction" OR "the density of the flux of magnetic induction". Actually, it is the same thing:

B - magnetic induction;
(B, dS) - elementary flux of magnetic induction;
(B, dS)/dS = B - the density of the flux of magnetic induction OR just magnetic induction.

The same is when we talk about the electricity.
D - electric induction OR electric induction flux density.

Sorry, I must go to university,... I will end this post when I come back.

3. Oct 29, 2009

### ApexOfDE

Both of formulas are correct. The problem is just that electric flux density is other name of electric displacement.

4. Oct 29, 2009

### wfunction

Thank you for the replies.

I still don't understand the answer, though. I know this is a technicality, but there is only one official unit for electric flux, and so my question is what that unit is. Is it volt-meters, coulombs, or something else?

Thanks!

5. Oct 29, 2009

### Born2bwire

There is no accepted unit of flux that I have seen. Normally, we take the electric flux to be the surface integral of the electric field, and you would be hard pressed to find a differing convention. But, on a few occasions (like in the CRC Handbook it turns out), flux is sometimes taken as the surface integral of the electric flux density. The latter maybe a more useful definition since it will always result in the total enclosed charge for a closed surface, regardless of the background permittivity. But since we so often work with a homogeneous volume when computing a closed surface flux, the ratio of charge to epsilon is often taken too.

6. Oct 29, 2009

### ApexOfDE

As I said above, electric flux and electric flux density (electric displacement) are different parameter. Therefore, they have different units.

Can you tell me an article shows that electric flux density's unit is V/m? Because D = epsilon * E ==> D(unit) >< E(unit)

I think you are confused with the name of D.

7. Nov 12, 2009

### cubdh

There is no need to complicate matters.
Electric Flux = # of Coulombs of charge or "C" for coulombs.

Electric Flux density is the C/m2 or Coulombs per meter sq.

These are all in SI units.