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

[bengaltiger14]

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?

 

[Physics_Math]

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.

 

[LowlyPion]

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?

 

[bengaltiger14]

Still not getting correct answer. Lowly, you are saying the disregard the x hat and z hat component right?

 

[LowlyPion]

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) = ...