# Use Gauss’ law to derive this (23-13) equation. Please show steps. Gauss' Law: Planar Symmetry Sheet...

###### Question:

Use Gauss’ law to derive this (23-13) equation. Please show steps. Gauss' Law: Planar Symmetry Sheet 7 shows a portion of a thin, infinite, nonconducting s ve) surface charge density ơ.A sheet of thi one side, can serve as a simple model. Le n front of the sheet. ing heet with a uni- plastic wrap, uniformly t us find the electric field Gaussian surface is a closed cylinder with end caps of are ierce the sheet perpendicularly as shown. From symmetry, E must lar to the sheet and hence to the end caps. Furthermore, since the tive, E is directed away from the sheet, and thus the electric field e two Gaussian end caps in an outward direction. Because the field erce the curved surface, there is no flux through this portion of the ce. Thus E . dA is simply E dA; then Gauss' law, a A, charge enclosed by the Gaussian surface. This gives E 2ε (sheet of charge). (23-13) idering an infinite sheet with uniform charge density, this result t at a finite distance from the sheet. Equation 23-13 agrees with e found by integration of electric field components. tive view portion of a sheet, uni- side to sur- A closed rface passes Gaussian tsurface ttt There is flux on

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