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Vector area of a surface S

  1. Jun 18, 2011 #1
    Define

    [itex]\textbf{a}\equiv\int_{S}{d\textbf{a}} [/itex]

    How do I show that [itex]\textbf{a}=\frac{1}{2}\oint{\textbf{r}\times d\textbf{l}}
    [/itex]

    Actually, this is the problem of the EM book of Griffiths, but I don't understand his hint.

    Any help would be appreciated.
     
  2. jcsd
  3. Jun 19, 2011 #2
    One trick is to dot the latter expression with an arbitrary constant vector, and then use cyclicity of the triple product. You should be able to cast it into a form where it is easy to use Stokes' Theorem.
     
  4. Jun 19, 2011 #3
    O.K., I got the result.

    But is there any other more physical or geometrical way to derive that?

    Thanks!
     
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