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Math Help - Flux of vector field

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    Flux of vector field

    How do you calculate the flux of the vector field F=xi+yj+zk across a disk x^2+z^2\leq 1 in the plane y=3 with the normal vector pointing in the y direction
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    Quote Originally Posted by pkrleads View Post
    How do you calculate the flux of the vector field F=xi+yj+zk across a disk x^2+z^2\leq 1 in the plane y=3 with the normal vector pointing in the y direction
    The unit normal vector to the disk is \vec{n} = \hat{j}

    So by definition

    \iint \vec{F}\cdot d\vec{S}=\iint \vec{F} \cdot \vec{n}dS

    Where dS is the projection of the disk into the x-z plane

    \iint_DydA but on this disk y is constant and y=3

    3\iint_DdA since the integrand is constant the value of the integral is

    3\pi
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