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Math Help - Potential Function of a Vector Field

  1. #1
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    Potential Function of a Vector Field

    Alright so I have no idea what im doing and I cant seem to figure it out

    from what I can tell a vector field is generally, although not always, just the gradient of the potential field

    so I have this question to answer:
    Find a potential for the vector field F by inspection.
    F = <yz^2,xz^2,2xyz>

    i thought it would simply be phi(x)=xyz^2
    thought this is not that case
    what am i doing wrong?
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  2. #2
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    If I understand this you're looking for a function \phi (x,y,z) such that \nabla \phi(x,y,z)=F(x,y,z). If this is the case, simply derive and check that your answer is correct (It is, if this is what you meant anyway).
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  3. #3
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    Quote Originally Posted by TheUnfocusedOne View Post
    Alright so I have no idea what im doing and I cant seem to figure it out

    from what I can tell a vector field is generally, although not always, just the gradient of the potential field

    so I have this question to answer:
    Find a potential for the vector field F by inspection.
    F = <yz^2,xz^2,2xyz>

    i thought it would simply be phi(x)=xyz^2
    thought this is not that case
    what am i doing wrong?
    I assume a scalar potential is required. In which case your answer is correct. Why do you think it's wrong? (Note: The question says "Find a ....", not "Find the ..." If it was "Find the ..." then you would have to add a constant to your answer).
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