Flux of Vector Field F out of Cube: 1

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    Cube Flux
In summary, a flux is a measure of the flow of a vector field through a given surface or region, representing the amount of the field that passes through the surface per unit time. A vector field is a mathematical concept that describes a quantity, such as velocity or force, that varies in space. Flux is calculated by taking the dot product of the vector field and the normal vector to the surface, and then integrating over the surface. The flux of a vector field is important for understanding physical phenomena and making predictions about future behavior. Finding the flux out of a cube involves calculating the amount of the vector field passing through the six faces of the cube, which is useful in applications such as fluid dynamics or electromagnetism.
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sci-doo
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Homework Statement


What is the flux of vector field F = xi + zj out of the cube that has corners in (0,0,0),(1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1).

The Attempt at a Solution


Is it 1?

Divergence = del dod F = 1
Triple integral of divergence= SSS 1 dx dy dz each from 0 to 1
= 1

I don't have a solution for this one, so I'd like to know if I got it right. :smile:
 
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  • #2
Yes, it's 1.
 
  • #3
Tom Mattson said:
Yes, it's 1.

Thanks!
 

What is a flux?

A flux is a measure of the flow of a vector field through a given surface or region. It represents the amount of the field that passes through the surface per unit time.

What is a vector field?

A vector field is a mathematical concept that describes a quantity, such as velocity or force, that varies in space. It is represented by a vector at each point in space.

How is flux calculated?

Flux is calculated by taking the dot product of the vector field and the normal vector to the surface, and then integrating over the surface. This gives the total amount of the vector field that is passing through the surface.

Why is the flux of a vector field important?

The flux of a vector field is important because it provides information about the flow of the field through a given region. This can be helpful in understanding physical phenomena and making predictions about future behavior.

What does it mean to find the flux out of a cube?

Finding the flux out of a cube means calculating the amount of the vector field that is passing through the six faces of the cube. This can be useful in applications such as fluid dynamics or electromagnetism.

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