Understanding Zero and Nonzero Flux: A TA's Analogy

In summary: So, in summary, when there is a flux through a surface without boundary (enclosing a volume), the flux is the integral of the normal component of the vector field (wrt the surface) over the surface.
  • #1
StephenPrivitera
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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?
 
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  • #2
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
 
  • #3
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.
 
  • #4
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."
 

1. What is flux and how does it relate to zero and nonzero flux?

Flux is a term used in physics to describe the flow of a physical quantity through a surface or boundary. In the context of zero and nonzero flux, it refers to the amount of a physical quantity passing through a surface. Zero flux means that no quantity is passing through the surface, while nonzero flux means that there is some amount of the quantity passing through the surface.

2. Can you give an example of zero and nonzero flux?

Imagine a room with two open windows. If there is no wind blowing, the air inside the room is still and there is zero flux of air passing through the windows. However, if a strong wind blows, there will be nonzero flux of air passing through the windows.

3. How can I understand the concept of flux better?

An analogy that may help in understanding flux is to think of it as a flow of water. Zero flux would be like a still pond with no water moving, while nonzero flux would be like a river with a strong current. Visualizing flux in this way can help in understanding its behavior and properties.

4. What is the role of a TA in helping students understand zero and nonzero flux?

A TA's role is to assist students in understanding complex concepts and to provide analogies, examples, and explanations to aid in their understanding. In the context of zero and nonzero flux, a TA can use various teaching methods to help students grasp the concept, such as demonstrations, visual aids, and guided practice problems.

5. Why is it important to understand zero and nonzero flux?

Understanding zero and nonzero flux is crucial in many fields of physics, including electromagnetism, fluid mechanics, and thermodynamics. It allows for the calculation and prediction of various physical phenomena, such as electric and magnetic fields, fluid flow, and heat transfer. It also helps in understanding the behavior of natural processes and in designing technological systems.

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