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Math Help - Vector field question

  1. #1
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    Vector field question

    A vector function F is not irrotational.Show that it is always possible to find a scalar function f so that the function fF is irrotational.

    A vector field V is not irrotational.Show that it is always possible to find f such that fV is irrotational.

    X[fV]=fxV-Vxf
    V is not irrotational means:

    curl(V)=U
    U
    non equal to zero.

    f
    V irrotational means:
    curl(fV)=0

    But:
    curl(fV)=grad(f)xV+fcurl(V)=grad(f)xV+f U

    So you get:

    grad(f)xV+f U=0
    grad(f)/f xV+ U=0
    grad(ln(f))xV=-U

    Then,what should I do?

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  2. #2
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    Quote Originally Posted by kolahalb View Post
    A vector function F is not irrotational.Show that it is always possible to find a scalar function f so that the function fF is irrotational.
    Chose f(x,y,z)=0
    What is the problem?
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  3. #3
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    The problem is to find f(x,y,z) to prove that X[fV] can be made equal to zero even if X[V] is not zero.
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  4. #4
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    Quote Originally Posted by kolahalb View Post
    The problem is to find f(x,y,z) to prove that X[fV] can be made equal to zero even if X[V] is not zero.
    I did! The curl of the zero vector is a zero vector. Right?

    So given any irrotational vector field.
    If you multiply it by f(x,y,z)=0 then it because a zero vector. Whose circulation is a zero vector. Hence the scalar function is always zero.

    My construction is trivial. But there is nothing in your question which forbids me from using that.
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  5. #5
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    The examiner will not be pleased with this trivial answer.So,please try seriously.
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  6. #6
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    Quote Originally Posted by kolahalb View Post
    The examiner will not be pleased with this trivial answer.So,please try seriously.
    I will try tomorrow. Now I have to leave. But again there is nothing in the question which forbids that.

    That is what I hate about engineering classes. They never, ever pay to attention to divison by zero and trivial cases. That is their problem.
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