Active Figure 24.4 A Closed Gaussian Surface The animation below shows a closed

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Active Figure 24.4 A Closed Gaussian Surface The animation below shows a closed Gaussian surface that lies in an external electric field. The orange electric field lines are due to charges that lie outside of the surface, so each field line entering the surface eventually passes back out. For example, one electric field line enters into the surface at the point labeled 3, and then leaves the surface at the point labeled 1. At the point labeled 2, the electric field line just grazes the surface Instructions: Click the points labeled 1, 2 and 3 to see a diagram that explains the sign of the outward electric flux through a small region surrounding the point Explore For a constant and uniform electric field E, the electric flux that passes through an area A is given by the following equation, where is the angle between the electric field E and the outward unit normal n In the animation, we follow convention and give the area of a small patch of surface a vector direction. The area vector A is a vector with magnitude equal to A and direction given by the outward unit normal A=An To calculate a value of the outward electric flux through a closed surface such as the one above, we subdivide the entire surface into small patches each with area A. The area of each patch is chosen to be small enough so that the area is essentially flat and the electric field is essentially constant and uniform over the extent of A. In this case, Equation (1) above gives the outward electric flux through each area A AA1 E Display in a New Window The value we calculate for Equation (1) depends on which patch we use for the calculation. For example, click patch 1, and notice that electric field pierces out of the surface over the area A1. In this case, 0

Explanation / Answer

Closed surface contains net positive charge   : More Filed lines leave than enter

Closed surface contains net negative charge   : More field lines enter than leave

closed surface contains no charge           : Every field line that enters also leaves

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