Understanding Zero and Nonzero Flux: A TA's Analogy

[StephenPrivitera]

My TA gave this analogy of a guy with a machine gun. He drew two boundaries. He said, 100 bullets pass through both boundaries per second. So in the space between the two boundaries, there is a zero flux. (?) But if there is a guy standing in between the two boundaries and he gets shot with three bullets per second, then there is a nonzero flux because there is not an equal amount of bullets coming passing through each boundary. (?)

What does it mean that there is a zero or nonzero flux between the two boundaries? I thought that flux was the rate a which something passes through a unit area. I don't understand the idea of a flux in some sort of space. I understand the ideas of flux at each of the boundaries just not when you throw the guy in the middle.

He also mentioned a river analogy that he said was simpler, buthe didn't explain it to me. Anyone know what analogy this is?

 

[chroot]

The flux of something through a volume is the number of those somethings entering per unit time, minus the number of those things leaving per unit time.

In the volume between the two boundaries, the same number of bullets leave as enter -- in a large enough unit of time, say, a minute.

When the victim absorbs some of those bullets, there are fewer leaving than entering per unit time, so there is a nonzero flux.

- Warren

 

[vanesch]

OK, what chroot writes is correct concerning the flux through a surface without boundary (enclosing a volume), when the vector field is a current density. In general, a flux is a combination of a vector field and a surface: it is the integral of the normal component of the vector field (wrt the surface) over the surface.
In LaTeX notation:
\int dS \bf{n(S)} \dot \bf{V}(S)

cheers,
Patrick.

 

[StephenPrivitera]

Originally posted by chroot
The flux of something through a volume is the number of those somethings entering per unit time, minus the number of those things leaving per unit time.

In the volume between the two boundaries, the same number of bullets leave as enter -- in a large enough unit of time, say, a minute.

When the victim absorbs some of those bullets, there are fewer leaving than entering per unit time, so there is a nonzero flux.

- Warren

That makes things much clearer. It seems as though flux is defined differently for a surface and a volume. I asked my TA if this flux in the volume is considered a delta flux. He said, "Well, yeah, but that's an overly complicated way of thinking about it."