Flux through a cylindrical wedge surface

In summary, flux is the measure of the amount of a physical quantity passing through a surface, represented by the symbol Φ. It is calculated by taking the dot product of the vector field and the normal vector of the surface, and then integrating this dot product over the surface. Finding flux through a surface is important in various fields and can help solve real-world problems. The units of flux depend on the physical quantity being measured, and it can be negative when the vector field is flowing in the opposite direction of the surface's normal vector or when a physical quantity is leaving the surface.
  • #1
Rombus
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Homework Statement



If vector [itex]A=(2x,-z^2,3xy)[/itex], find the flux of A through a surface defined by [itex] ρ
=2, 0<\phi<\pi/2, 0<z<1[/itex]

Homework Equations



divA?

The Attempt at a Solution


Can I use divergence here?
This is a closed surface correct? Is this is a cylindrical wedge?
Also do I need to convert the vector field to cylindrical form? Or the defined surface to rectangle form?

If I used divergence do I divide my answer by 4 since the wedge is a 1/4 of the cylinder?

Thanks
 
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  • #2
Is this question in the wrong forum? Any help would be appreciated.
 

1. What is flux through a surface?

Flux is the measure of the amount of a physical quantity passing through a surface. In the context of vector fields, flux is the measure of the flow of a vector field through a surface. It is represented by the symbol Φ.

2. How is flux through a surface calculated?

Flux through a surface is calculated by taking the dot product of the vector field and the normal vector of the surface, and then integrating this dot product over the surface. The resulting value is the flux through the surface.

3. Why is finding flux through a surface important?

Calculating flux through a surface is important in many areas of science and engineering, such as fluid mechanics and electromagnetism. It helps us understand the flow of physical quantities through different surfaces and can aid in solving various real-world problems.

4. What are some common units for flux?

The units of flux depend on the physical quantity being measured. For example, the units for electric flux are coulombs per square meter, while the units for fluid flux are cubic meters per second per square meter. Other common units include watts per square meter for radiant flux and lumens per square meter for luminous flux.

5. Can flux through a surface be negative?

Yes, flux through a surface can be negative. This occurs when the vector field is flowing in the opposite direction of the surface's normal vector. In this case, the dot product will be negative, resulting in a negative flux value. Negative flux can also represent when a physical quantity is leaving the surface instead of entering it.

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