# Intuitively, how do you explain the concept of Flux?

Lately in my physics and mathematics classes, I've come across the concept of Flux. And although I've been able to define them mathematically and figure out how to use them. I'm still not entirely sure what flux is.

My question is:

So is there any intuitive way I can understand the concept of flux?

• Let me just say that flux is not what "Back to the Future" made it seem! Unfortunately. – Asaf Karagila Sep 12 '14 at 21:33
• Flux is the flow of a physical property in space. For instance the heat flux from a hot surface. – Mhenni Benghorbal Sep 12 '14 at 21:39
• Read "Div,Grad,Curl and all That" by Schey: amazon.com/Div-Grad-Curl-All-That/dp/0393925161 – Alex R. Sep 15 '14 at 20:38

I recall hearing flux described as the amount of rain passing through an open window. Depending on the direction of the rain and the orientation of the window, all of the rain, some of the rain, or none of the rain may pass through.

Edit:

For example, consider a rainstorm where every raindrop is coming perfectly straight down, and you have an open window on your roof that is perpendicular to the direction of the rain. The flux would be exactly equal to the rate of water entering your home divided by the area of your window. If rain somehow stayed perfectly still after striking your floor, you would have a puddle of rain exactly the shape of your window on your floor.

Now, lets change the orientation of the window--say the same size window is now open on the side of an angled roof. If the rain is coming straight down, the magically immobile puddle on your floor would be smaller. It would be the projection of the shape of your window onto the plane perpendicular to the rain. The flux would be equal to the rate of water entering the home divided by the area of this projection.

Now, lets change the orientation of the window again -- say its now on one of your walls. Since the rain is coming straight down, no rain would enter your window since the opening is parallel to the rain. Since no rain is entering the home, the flux is zero.

The same analogy holds with more complicated rain patterns and window shapes. The trajectory of the raindrops is analogous to a vector field, and the window is analogous to any arbitrary surface on which you want to calculate the flux.

• Could you possibly expand a bit more on this? I'm having a bit of trouble visualizing how it would work or a simple example of numbers or such? – Rivasa Sep 15 '14 at 16:54

Flux means flow. If you imagine a collection of moving particles distributed in space, the particle flux is the rate at which those particles pass through a given surface or opening (number of particles per second).

Flux is a particularly useful concept for vector fields obeying the inverse square law. Consider a mass of particles streaming out from a point source at a constant rate and travelling at a constant speed. The flux of particles through any sphere centred on the source must equal the rate at which the particles are being generated at the source. Because the surface area of such a sphere (radius $r$) is $4\pi r^2$, the flux density (flux divided by area) falls off as $1/r^2$ - an inverse square law. Now distort that sphere to any shape you like, while taking care to ensure it still contains the source. The total flux (flow) through it must still equal the rate at which particles are being generated. And this is true for the flux associated with any inverse square law field. That's Gauss's Law, a powerful principle in the theories of electrostatics and gravitation.

Simply: Flux is the amount of flow entering a surface straight on.

Less Simple: Flux is the amount of flow through a surface in the direction of its normal vector (vector perpendicular to its surface).

Example:
Imagine a pipe carrying water. This pipe has a flow through it measured to be 5 L/sec. Now imagine a mesh screen intersecting the pipe. The flux through this screen is 5 L/sec. Now imagine having the screen intersecting the pipe at an angle. The screen still has 5 L/sec flowing through it, but its flux is < 5 L/sec because not all the water is flowing through at head on (water is entering at an angle to the normal vector). If you placed this screen into the pipe so that it ran parallel with the flow of water, the flux through the screen is zero, because there is no water flowing through the screen.

• IMO this is wrong. As long as the screen is intersecting the pipe, the total flux through it must be 5 L/sec, whatever angle it takes (except parallel). Because: flux = velocity projection on normal times area. And the latter is also changing with the normal (the other way around). – Han de Bruijn Sep 15 '14 at 15:27