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Question on Gauss's law

  1. Feb 4, 2012 #1
    This is not a homework question.

    I'm just having trouble understanding when it's appropriate to apply Gauss's law or not, and under what conditions does it fail.

    For example, suppose I have two point charges forming a dipole. If I draw a cylinder around them, then the total charge enclosed is zero, implying that the field is zero.

    However, this is obviously not true for a dipole.

    So would I be using Gauss's law incorrectly in this case, or does it not applying to discontinuous charge distributions, or what?
  2. jcsd
  3. Feb 4, 2012 #2
    No, it implies that the closed surface integral of a certain projection of the electric field is zero. Not that the field is zero at each point on the enclosing surface.
  4. Feb 4, 2012 #3


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    Gauss's Law would say ##\oint \vec{E}\cdot d\vec{S} = 0##. This means the electric flux into a volume is balanced by the electric flux out of the volume. It doesn't mean ##\vec{E}=0##, which would mean there is no electric flux at all into or out of the volume.
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