What is the correct method to find the flux of a vector field through a surface?

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    Flux Integral
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Homework Help Overview

The problem involves calculating the flux of a given vector field through a specified surface. The vector field is defined in terms of its components, and the surface is constrained within certain limits for the variables x, y, and z.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to compute the flux by integrating the components of the vector field directly. Some participants question whether the method used is appropriate for calculating flux, suggesting that the original approach may not align with standard flux integral methods.

Discussion Status

Participants are actively discussing the correct approach to calculating the flux integral. Some guidance has been offered regarding the importance of considering only the relevant components of the vector field that contribute to the flux through the surface. There is an ongoing exploration of how to properly set up the integral.

Contextual Notes

There appears to be confusion regarding the contributions of different components of the vector field to the flux calculation, particularly whether to include or disregard certain components based on their orientation relative to the surface.

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Homework Statement



A vector field is given by: A=2x(x hat) + 3(y hat) + 2y(z hat). A surface S is defined by 0<=x<=2m, y=5m, 0<=z<=2m. Find the flux of A through S.


I plug the 5m into the z hat term to get 10(z hat) and then integrate.

Integrating the (x hat) term I get 4. The y hat term comes out because it is constant. Integrating the z hat term to get 20. Sum those up and I get 27.

The actual answer is 12. Can anybody tell me what is wrong?
 
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What you are doing is simply computing the anitderivative of the vector field. That is not how to calculate a flux integral. There are several ways to compute flux integrals of which you should look up. If the surface is closed (e.g. a sphere) you can use the divergence theorem otherwise known as Gauss's law. Otherwise there are more standard ways to calculate the flux integral. Perhaps if you have a textbook you should read the section that explains flux integrals.
 
With flux you are interested in the component of the flux passing through the surface aren't you? So won't any components of the flux lying in the plane of the integral not contribute? So doesn't that suggest that you can ignore the contribution of the x and z components?
 
Still not getting correct answer. Lowly, you are saying the disregard the x hat and z hat component right?
 
bengaltiger14 said:
Still not getting correct answer. Lowly, you are saying the disregard the x hat and z hat component right?

Yes.

And now integrate the y component across the area of the x-z planar surface.

3*(2*2) = ...
 

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