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Homework Help: Vector field, Conservative?

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data

    For what value(s) of the scalar 'a' is the vector field
    F(x,y,z)= 2xz i + ay^3 j + (x^2 + y^4) k conservative



    3. The attempt at a solution

    F1=2xz
    F2=ay^3z
    F3=(x^2 + y^4)

    I used 3D curl test??

    1)(partial F2)/(partial dx) - (partial F1)/ (partial dy)= 0-0 = 0
    2)(partial F3)/(partial dy) - (partial F2)/ (partial dz)= 4y^3 - ay^3=0 so a=4
    3)(partial F1)/(partial dz) - (partial F3)/ (partial dx)= 2x-2x = 0

    my answer would be a=4
     
  2. jcsd
  3. Dec 8, 2008 #2

    Defennder

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    Homework Helper

    If your Fy is supposed to be ay^3z then you're right. Your initial statement of the problem has Fy = ay^3.
     
  4. Dec 8, 2008 #3
    yes it should be ay^3z j, Thanks!
     
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