Application of Gauss\' law: finding the electric field near a sheet of charge A

Question

Application of Gauss' law: finding the electric field near a sheet of charge A large sheet bas charge density (this is the charge in each unit of area.) A cylindrical G aussian surface encloses a portion of the sheet and extends a distance L on either side of the sheet. A1.A2. and A3 are the areas of the right end, left end and curved side, respectively. Only a small portion of the sheet is shown. On the diagram at right use your pencil to shade in the charge enclosed by the Gaussian cylinder. In terms of and other relevant quantities. what is the net charge enclosed by the Gaussian cylinder?

Explanation / Answer

If is the charge per unit area in the plane sheet, then the net positive charge q within the Gaussian surface is

q = A

So the net charge depends on the two factors

1. Charge density

2. Area enclosed by the Gaussian surface

According to this we can shade the charge enclosed by the Gaussian cylinder

Shade the portion, in which the Gaussian cylindrical surface pass through perpendicular to the plane sheet, not the remaining portion of the sheet

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