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Thread: Determine the Potential Function

  1. #1
    Senior Member bugatti79's Avatar
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    Determine the Potential Function

    Folks,

    Find the potential function for $\displaystyle F(x,y)=-2xy^3 \vec i -3x^2y^2 \vec j$

    IF we take $\displaystyle \phi_x= -2xy^3$ and $\displaystyle \phi_y=-3x^2 y^2$

    Integrating the first one wrt x gives

    $\displaystyle \phi (x,y)=\int -2xy^3 dx = -x^2 y^3 +k(y)$

    Differentiating the RHS wrt y gives

    $\displaystyle -3x^2y^2 +k'(y)$ but

    $\displaystyle \phi_y=-3x^2 y^2 \implies k'(y)=0 \implies k(y)=C$

    $\displaystyle \phi(x,y)=x^2y^3+C$........?

    If I apply $\displaystyle \nabla \phi$ is end up with the vector field F above.
    Last edited by bugatti79; Jan 14th 2012 at 10:53 AM. Reason: Found answer
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