Gauss’s Law

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Section 9.12 Gauss’s Law

Principle 9.12.1. Gauss’s Law.

The net electric flux through any closed surface is equal to the charge enclosed by that surface divided by $\epsilon_0\text{:}$

\begin{equation*} \mathit{\Phi}_E = \frac{Q_{enc}}{\epsilon_0} \end{equation*}

\begin{equation*} \bigcirc \!\!\!\!\!\!\!\!\!\iint_S \vec{E}\cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} \end{equation*}

Exercises Activities

Figure 9.12.2. Several charge distributions and Gaussian surfaces. The circles represent spheres, and the square represents a cube.

1.

Rank the four cases above by the net electric flux through the shown Gaussian surface from greatest to least. Explain your reasoning.

2.

Suppose you have a straight wire with a uniform charge density, where the length of the wire is much, much greater than its width. What kind of Gaussian surface do you think you should choose for this charge distribution? Explain your reasoning.

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