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week3_chapter24_web - Gauss Law Gauss Law can be used as an...

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Week 3: Chapter 24 Gauss’s Law Gauss’ Law Gauss’ Law can be used as an alternative procedure for calculating electric fields. Gauss’ Law is based on the inverse-square behavior of the electric force between point charges. It is convenient for calculating the electric field of highly symmetric charge distributions. Gauss’ Law is important in understanding and verifying the properties of conductors in electrostatic equilibrium. Introduction Electric Flux Electric flux is the product of the magnitude of the electric field and the surface area, A , perpendicular to the field. Φ E = EA Units: N · m 2 / C Section 24.1 Electric Flux, General Area The electric flux is proportional to the number of electric field lines penetrating some surface. The field lines may make some angle θ with the perpendicular to the surface. Then Φ E = EA cos θ Section 24.1 Electric Flux, Interpreting the Equation The flux is a maximum when the surface is perpendicular to the field. θ = 0 ° The flux is zero when the surface is parallel to the field. θ = 90 ° If the field varies over the surface, Φ = EA cos θ is valid for only a small element of the area. Section 24.1 Electric Flux, General In the more general case, look at a small area element. In general, this becomes The surface integral means the integral must be evaluated over the surface in question. In general, the value of the flux will depend both on the field pattern and on the surface. cos E i i i i i E A θ    E A 0 surface lim i E i i A E E A d   E A Section 24.1
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