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Pacopag

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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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