Vector Calculus: Understanding Flux

mazza aagaya yaar, thanks

Awesome page!! So well explained! Thank you :slight_smile:

The only thing that bugs me is…
which is greater the negative flux of the zero one? please answer

Negative flux means something is entering the region, like pouring water into a bucket. Zero flux means nothing is entering or leaving, like trying to pour water into a bucket that is sideways (nothing enters).

From a human perspective, what we call “negative flux” is typically better than zero flux. It depends on the scenario.

Hi Cassandra, you’d want to measure the flux from each of the sources (one at a time) and take the largest.

@Tamim: Here, A represents a unit of area and “n” represents the normal vector.

I’ve got a glimpse about flux in high school physics (Electric flux and Gauss Law of E. fields without even using regular calculus). I thought a little and understood flux in a way. Tell me if those are correct. (I have yet to study Vector calculus in undergrad)

  • Why flux is used in physics?: Fields are creepy. We are not very used to force-at-a-distance. Imagine trying to touch ur friend and getting repelled by some kind of mysterious force, how creepy is that? But the same thing happens in electromagnetism, so we are not very happy about it. On the other hand, you try to touch a working table-fan and you feel it pushing u away at a distance. We don’t freak out, bcz we know that fan is pushing (emitting) the air and the emitted-yet-invisible air is pushing us away.

So, we are trying to use the same analogy in fields. We feel better in assuming that a charge is ‘emitting’ something, and that something pushes another like charge near it. Of course, we know that charge isn’t actually emitting anything, bcz it’s energy is not reducing with time. But we love to think of it that way. We call this imaginary ‘something’ that’s emitted: Flux.

To understand the implications of Gauss law (Flux depends ONLY in the charge inside. Not the charges outside, not the position of the charge inside, not the size of surface…), I imagine the charge as the sun. Sun emits power (energy per unit time) in all directions, just like the charge emits flux. (Although flux is imaginary & power is real). If we draw an imaginary closed surface around the sun, the TOTAL power passing through surface doesn’t depend on whether the sun is in the center of the surface or not. Also, it won’t depend on the size of surface. A surface with smaller radius will have high intensity (power per unit surface area) but will have the same TOTAL power passing through it. Now, If we place the sun outside the surface, all the power that passes inside will pass outside. So we can say, the NET total power through the surface is zero. And that are the implications of the Gauss law.

To understand the concept that [flux = field intensity x area x cos(orientation angle)], I like to think flux as river flow (sun’s energy is radiated spherically, so can’t take it as analogy here) as u said. orientation of the bucket decides how much water is collected.

PLEASE REPLY ME TELLING IF EACH OF THIS UNDERSTANDING IS CORRECT.

@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 :slight_smile:

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 :)).