@Abarajithan: Yes, that’s essentially correct. Gauss’ Law says you can’t “lose” flux so no matter your surface, you’ll be seeing the net amount contained inside.
However, the law only works for fields that diminish with radius squared (which is the case for electric and gravitational fields).
See this older article for more details:
http://www.cs.princeton.edu/~kazad/resources/math/Gauss/gauss.htm
Thanks !!!
This is too elaborate and comprehensive
You should write a series of books on all forms of math, specially the higher level stuff. I know I’d buy them.
Thanks David, hoping to get a few more books out there down the line :).
$$\displaystyle{\Large \int_{A} F(x) \cdot n \ dA} $$
where did this n came from here ?? you didn’t explain that.
@Ondřej Kubů
True, however when considering the history of classical physics, fields and flux were introduced as mathematical tricks to solve certain problems, right? Later, we realized that these are more real than the things we consider “real” in classical physics.
Thanks Kalid! That makes sense 
If a flow line passes through a surface that is at an angle to the flow line (like your the Partial Flux picture in the article), why do we say that only component of the flow that is parallel to the area vector goes through the surface? Doesn’t it ALL still hit and PENETRATE the surface? Why do we treat this surface as though it only allows things oriented perpendicular to itself to pierce through?
Or, to use the intuitive language of this page, say I have a ladder leaning against a wall at some angle with the horizontal. I stand on the ground and fire a bullet (or throw a banana?) horizontally at the ladder, aiming to make sure that it will pass in between the steps of the ladder to go through to the other side. Surely when I fire the bullet, the whole bullet passes through the line of ladder, not just some cos(a) component of the bullet?
@Ron: Great question. I used the analogy of bananas to help visualize flux, but it’s really about microscopic forces and surfaces.
Imagine a bunch of thin pipes (1 atom wide) that carrying water. Depending on the angle, we might intersect a larger or smaller number of pipes:
For example, the perpendicular surface gets 3 pipes, but the angled one only gets 2. If we imagine the pipes taking up all the space in-between, we can capture any fraction between 0 and 100%. Hope that helps.
@Abarajithan
Your claim about charge emitting nothing is not correct. According to quantum mechanics, we understand all physical interactions as caused by co called virtual particles that are emitted and absorbed by the matter. We cannot see (or measure, to be precise) the particles but we can measure the forces which the particles cause when they are emitted or absorbed.
Flux is maximum if electric field lines are parallel to vector area but minimum when they are parallel to common area?
Pls help
Guys, guys,… you all get “D with big minus”!!!
Flow is an integral of Flux over some surface!!! Thus it means than FLUX is a density of FLOW.
Flux SHOULD (but ofcorse not usually) have units of “X per area per time” (where can be enything. Lets have X=number of Apples)
So lets have a Surface(S) with area (A) and lets we be given that a flux of apples is equal to 3 over that surface. That means that THROUGH EVERY POINT of a S and every instanse of Time 3 apples pass.
Lets calculate the FLOW of apples across that S.
Flow = Integral of Flux over surface.
i.e. Flow = TOTAL FLUX (as some people say)
@manuka: It’s a good point. In the intro of that same Wiki article: “The terms “flux”, “current”, “flux density”, “current density”, can sometimes be used interchangeably and ambiguously, though the terms used below match those of the contexts in the literature.”
It seems in some physics contexts, like heat transfer, flux is assumed to be “per unit area” and in math contexts it’s simply a vector that’s used in a surface integral (essentially a double integral). Rather than insist on a certain definition we should learn what concept is actually being pointed to. (It reminds me of what base “log” is supposed to mean [without any base specified]. It’s base 10, base e, or base 2 depending on the field :)).
P.s.
Flux units = X per AREA per TIME
Flow units = X per Time (usually it should mean that this Flow is taken over SOME AREA but not “dA”(not infinitesimal area)
P.p.s.
Proof that there some poeple who thinks my way?
look here http://en.wikipedia.org/wiki/Flux
"Flux as flow rate per unit area"
But yes… Flux is very often is used as a synonim for FLOW… It really bugs me.
ok. Any karma to me? I accept donations…
Thank you very much, this way I’m learn, I should understand the intuition behind a topic.
You are brilliant.
I have gone up and down through soooo many google sites for vector calculus…this is the first one that made complete sense! Great analogies, thanks for the informal tone.
Thank you for putting this together, you’re a lifesaver!
It was fantestic.I am feeling very nice after study about flux on this site because the explanation was very nice and everything was clear.
How do I determine the net flux across the surface of the above described control volume (three dimensional control volume of uniform two dimensional cross section being the Kock snowflake and with the third dimension being a unit height)?
Hi Kalid, This is the first time I’ve found flux explained in a way that I can understand it. I might just be able to use the concept properly now and be able to calculate the flux in a variety of situations. I might also pass the Open University exam!
Anne, UK