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Math Help - Flux of a vector field through a cube

  1. #1
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    Flux of a vector field through a cube

    Calculate the flux of the vector field F = (4-x)i through the cube with verticies (0,0,0),(5,0,0),(0,5,0),(0,0,5), oriented outwards.




    First, I drew the cube. Since the vector field is only in the i direction, I eliminated all but two sides. Namely, the sides parallel to the x-axis. Is that a correct thing to do?

    Secondly, I noted that the only sides that are perpendicular to the direction of the vector field at any point have the following attributes:

    Surface #1: x = 0 at all points. Surface area = 25. This side is oriented towards -i.
    Surface #2: x = 5 at all points, surface area also 25. This side is oriented towards +i.

    Thus I figured it would be a simple problem of adding the fluxes through these two surfaces.

    Surface #1:
    Since x = 0 at all points, vector field F = 4i at all points on the surface. Since the orientation is -i, A vector = -25i.

    Dotting these two vectors is just -100.

    Surface #2:

    Since x = 5 at all points, vector field F = -i at all points on the surface. Since the orientation is +i, Area vector = 25i.

    Dotting these two vectors is -25.

    And,

    -100 + -25 = -125


    So, what part of this is incorrect thinking? Care to shed some light?


    Thank you!!
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  2. #2
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    Re: Flux of a vector field through a cube

    Can anyone help, please?

    Thanks!
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  3. #3
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    Re: Flux of a vector field through a cube

    So, I finally gave in a hit view solution. Lets observe.



    -_-
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