We are now in a position to actually evaluate a Gauss' law problem. The simplest application of Gauss' law is to derive the electric field for a point charge. Here's Gauss' law again:

\( \int_{S} \vec{E} \cdot \vec{dA}=\frac{Q_{enc}}{\epsilon_0} \)

where we now understand what all the pieces mean. The only ambiguity is which of the normal vectors to the area element \(d\vec{A}\) we should choose. In Gauss' law, by convention we choose the *outward* pointing normal.

We now turn to how to evaluate Gauss' law. Place a charge of magnitude \(\epsilon_0\) Coulombs at the origin. With Gauss' law you get to *choose* a surface \(S\) for which you want to integrate over to determine \(\vec{E}\). The surface that yields the easiest algebra for solving for \(\vec{E}\) using Gauss' law is

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