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Homework Statement
Is there an analog to Gauss's theorem (sorry about the title) in 2D.
The reason is to develop the continuity equation in 2D.
Homework Equations
In 3D it is.
[tex]\int_{S}{\bf A}. d{\bf S}=\int_{V}(\nabla . {\bf A})dV[/tex]
(please forgive my latex. A and dS should be vectors).
The Attempt at a Solution
I suppose we may extend the situation to 3d by allowing a little slice "out of the page" (so that our volume looks like a pancake) and just use the theorem as usual, while imposing that A does not have any component "out of the page", then afterwards take the thickness of the slice to go to zero.
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