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Divergence theorem

  1. Mar 23, 2013 #1
    1. The problem statement, all variables and given/known data
    The divergence theorem states that

    ∫∫∫V div F dV = ∫∫S F(dot)N

    Suppose that div F = 1, then

    ∫∫∫V div F dV = ∫∫S F(dot)N

    If divF = 2, does the following hold true?

    ∫∫∫V div F dV = 2∫∫S F(dot)N
    2. Relevant equations
    Since the divergence theorem computes the volume, if div F is a constant, then the volume formed by the closed surface would just be multiplied by that constant?

    3. The attempt at a solution
  2. jcsd
  3. Mar 23, 2013 #2


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    Science Advisor
    Homework Helper

    The divergence theorem always holds, the third equation doesn't hold. What is true is that if div(F)=1, then the volume integral is V. If div(F)=2 then the volume integral is 2V. You don't insert an extra constant into the divergence theorem.
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