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Math Help - potential function

  1. #1
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    potential function

    If I calculate the curl of a vector field and it's 0 is it guaranteed that it has a potential function??
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    Quote Originally Posted by TheRekz View Post
    If I calculate the curl of a vector field and it's 0 is it guaranteed that it has a potential function??
    Let F be a three dimensional differentiable vector field with continuous partial derivatives. Then
    \nabla\times F = 0
    if and only if F is conservative

    Vector potential - Wikipedia, the free encyclopedia
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  3. #3
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    I just need a yes/no answer.. I didn't get what you mean
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by TheRekz View Post
    I just need a yes/no answer.. I didn't get what you mean
    He did answer you question.

    If a vector field is conservative, then it is the gradient of some potential function.

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  5. #5
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    and it's conservative if the curl is 0
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    Behold, the power of SARDINES!
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    Quote Originally Posted by TheRekz View Post
    and it's conservative if the curl is 0
    Yes
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  7. #7
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    so indirectly saying my first statement is correct
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  8. #8
    Behold, the power of SARDINES!
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    Yes if the vector field satisfies the above hypothesis.
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