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Homework Help: Vector field

  1. Feb 2, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int[/tex] delxA dv = -[tex]\oint[/tex] Axds

    where A is a vector field
    Left hand side is integral over volume. Right hand side is integral over closed surface.

    2. Relevant equations

    3. The attempt at a solution

    Can't understand what Axds means.
  2. jcsd
  3. Feb 2, 2010 #2
    A is the vector field
    and dS is the closed surface on which you want to see the flux
    x is a multiplication symbol
  4. Feb 2, 2010 #3


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    Presumably what you are calling ds (which is usually used for an element of arc length) should be the vector surface element. If the surface is parameterized as

    [tex]\vec R = \vec R(u,v) = \langle x(u,v),y(u,v),z(u,v)\rangle[/tex]

    the surface element is

    [tex]d\vec S = \vec R_u \times \vec R_v\, dudv[/tex]
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