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On a Lemma of the Shell Theorem

  1. Jan 13, 2012 #1

    TMO

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    320px-Shell-diag-1.png

    I am concerned regarding a lemma of the shell theorem. Specifically, I am concerned with the idea that due to the vector nature of the forces, that one can simplify this:

    271c7a94be4496a99e2534e2ceae7751.png

    into this:

    63898081c163a2fc2c132f68be1bf017.png

    Could somebody precisely explain why we're allowed to multiply in the [itex]\cos \varphi[/itex] in the second equation?
     
  2. jcsd
  3. Jan 13, 2012 #2
    It's a dot product with the radius unit vector. You're projecting the contribution of dF (which I'm inferring is along s) along the radius vector r
     
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