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Math Help - Stokes

  1. #1
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    Stokes

    Can anyone help:

    Verify stokes theorem for the following vector field:

    A = (1+x(y^2))i + (x+2xyz+2)j + (sin z)k

    and the surface defined by (x^2)+(y^2)+(z^2)=25 where z>=3.

    Thanks.
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  2. #2
    TD!
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    It can be done in exactly the same fashion as this problem you posted a while ago

    It's completely the same question, method, manner of integration: only another area and vector field.
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  3. #3
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    still having problems

    Hello TD,

    I am still confused as to how you would do this question for two reasons:

    1) how do you recreate the vector r that you had when you answered my question last time?

    2) z is now >=3.

    Please help. Thanks.
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  4. #4
    TD!
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    Quote Originally Posted by jedoob
    1) how do you recreate the vector r that you had when you answered my question last time?

    2) z is now >=3.
    In the plane x = 3, which is now the ground plane (cfr. the xy-plane z = 0 from last time), the equation is x^2  + y^2  + 9 = 25 \Leftrightarrow x^2  + y^2  = 4^2 which happens to be the same circle as last time.

    The equation can be rewritten explicitly in function of z, because we know z is positive. We then have z = \sqrt {25 - x^2  - y^2 } which gives our r: \left( {x,y,\sqrt {25 - x^2  - y^2 } } \right)

    The fact that the minimum z is now 3 just means that you have to replace z by 3 where you replaced it by 0 last time.

    Note that it may be interesting to convert to other co÷rdinates, but it isn't necessary.
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  5. #5
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    curl F = 0????

    Hey,

    How do you go about doing a question using the method you applied previously but where curl F = 0.

    For example:

    Verify stoke for:

    F(x,y,z) = (x^2)i + (y^2)j + (z^2)k

    z=squareRoot[(x^2)+(y^2)] below the plane z=1.

    How do you avoid getting a zero surface integral?

    Please help, thanks.
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  6. #6
    TD!
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    Quote Originally Posted by jedoob
    How do you avoid getting a zero surface integral?

    Please help, thanks.
    You don't, since the integral will equal 0...!
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