# Divergence theorem

1. Mar 23, 2013

### randomcat

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. Mar 23, 2013

### Dick

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.