How Does Gauss's Law Apply to the Flux Through a Cube Near a Charged Sphere?

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In summary, the conversation discusses a homework problem involving a cube and a charged sphere, and the calculation of the total flux through the cube. The use of Gauss's law is suggested, and it is determined that the net flux through the cube should be zero. The importance of considering the orientation of the cube in the external field is also mentioned.
  • #1
physicsstooge
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I have the homework problem below with which I'm totally stumped. Can anyone out there help me out?

A small cube of volume 9.0 cm^3 is 0.30 cm from a metal sphere that has charge 3.00 coulombs. If the cube is empty, what is the total flux through it?
 
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  • #2
Consider Gauss's law.
 
  • #3
By "total flux", do you mean "net flux"? Like how much is leaving the cubical volume, versus how much is entering it? What do you think the answer is?
 
  • #4
"Consider Gauss's law."

I suppose the setup in this particular case that is confusing me. I'm probably making it harder than what it needs to be. I instinctively want to say it's the E * the Area of the cube, but that's not right.
 
  • #5
physicsstooge said:
"Consider Gauss's law."

I suppose the setup in this particular case that is confusing me. I'm probably making it harder than what it needs to be. I instinctively want to say it's the E * the Area of the cube, but that's not right.

You can calculate the flux through each one of the 6 sides of the cube that way. Did you re-check the question to see if it is talking about the net flux? What do they mean by "total" flux?
 
  • #6
physicsstooge said:
I instinctively want to say it's the E * the Area of the cube, but that's not right.
That's pretty close. More precisely, the net flux through the cube is the sum of [itex]\vec{E}\cdot\vec{A}[/itex] over the entire surface of the cube. What does Gauss's law tell you about the net flux through some volume?
 
  • #7
"What does Gauss's law tell you about the net flux through some volume?"


Sum should be zero. I knew I was making it harder than it was. Thanks guys
 
  • #8
Right! As long as the cube is empty (no charge inside), the net flux must be zero.
 
  • #9
physicsstooge said:
"What does Gauss's law tell you about the net flux through some volume?"


Sum should be zero. I knew I was making it harder than it was.

I'll just mention that some version of this problem is a favorite (often multiple-choice) exam question *precisely* because students may think that the external field is somehow important. The configuration of that field is often chosen to make calculating the flux through each surface of the cube very complicated. Thus, many students in desperation will select a choice thinking that there's supposed to be some clever way to do the flux integral, *rather* than realizing that they just want to apply Gauss' Law.

Just as a way to "psyche-out" such questions (related to useful approaches in physics problem solving generally), notice that nothing is said about the *orientation* of this cube in the external field of the charged sphere. (There's nothing in the statement of the problem that allows you to *assume* any symmetry.) How could these details *not* matter in finding the net flux? Only if the answer were the one where the external field didn't matter: zero.
 
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Related to How Does Gauss's Law Apply to the Flux Through a Cube Near a Charged Sphere?

1. What is total flux through a small cube?

The total flux through a small cube is the amount of energy, mass, or any other quantity passing through the cube per unit time. In other words, it is a measure of the flow of a physical quantity through the cube.

2. How is total flux through a small cube calculated?

The total flux through a small cube can be calculated by multiplying the area of the cube's face by the magnitude of the quantity passing through it per unit time. This calculation is based on the fundamental principle of flux, which states that the flux through a surface is equal to the product of the area of the surface and the component of the quantity perpendicular to the surface.

3. What factors affect the total flux through a small cube?

The total flux through a small cube is affected by several factors, including the size and shape of the cube, the magnitude and direction of the quantity passing through it, and the properties of the medium through which the quantity is passing. Other factors such as temperature, pressure, and concentration gradients may also impact the total flux.

4. What are some real-life applications of total flux through a small cube?

The concept of total flux through a small cube has many practical applications in various fields of science and engineering. For example, it is used to study the flow of fluids through pipes and channels, the movement of particles in a magnetic field, and the transfer of heat and mass in chemical reactions. It is also an important concept in understanding the behavior of electromagnetic waves and the distribution of energy in a given space.

5. How is total flux through a small cube related to conservation laws?

The concept of total flux through a small cube is closely related to the laws of conservation of energy, mass, and momentum. In many physical systems, the total flux through a small cube is conserved, meaning that the amount of a certain quantity entering the cube is equal to the amount leaving the cube. This fundamental principle is essential in understanding the behavior of various physical processes and phenomena.

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