Physics for Scientists and Engineers 8ed - ch24 - PowerPoint Slides

Physics for Scientists and Engineers 8ed - ch24 - PowerPoint Slides

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Chapter 24 Gauss’s Law
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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
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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
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Electric Flux, Interpreting the Equation The flux is a maximum when the surface is perpendicular to the field The flux is zero when the surface is parallel to the field If the field varies over the surface, Φ = EA cos θ is valid for only a small element of the area
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Electric Flux, General In the more general case, look at a small area element In general, this becomes cos E i i i i i E A E ∆Φ = = ⋅ ∆ Ε Α r r 0 surface lim i E i i A E E A d Φ = ⋅ ∆ Φ = Ε Α r r
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Electric Flux, final 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 The units of electric flux will be N . m 2 /C 2
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Electric Flux, Closed Surface Assume a closed surface The vectors point in different directions At each point, they are perpendicular to the surface By convention, they point outward i ∆Α r PLAY ACTIVE FIGURE
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Flux Through Closed Surface, cont. At (1), the field lines are crossing the surface from the inside to the outside; θ < 90 o , Φ is positive At (2), the field lines graze surface; θ = 90 o , Φ = 0 At (3), the field lines are crossing the surface from the outside to the inside;180 o > θ > 90 o , Φ is negative
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Flux Through Closed Surface, final The net flux through the surface is proportional to the net number of lines leaving the surface This net number of lines is the number of lines leaving the surface minus the number entering the surface If E n is the component of E perpendicular to the surface, then E n d E dA Φ = = Ε Α r r r r
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Flux Through a Cube, Example The field lines pass through two surfaces perpendicularly and are parallel to the other four surfaces For side 1, E = -E l 2 For side 2, E = E l 2 For the other sides, E = 0 Therefore, E total = 0
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Karl Friedrich Gauss 1777 – 1855 Made contributions in Electromagnetism Number theory Statistics Non-Euclidean geometry Cometary orbital mechanics A founder of the German Magnetic Union Studies the Earth’s magnetic field
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Gauss’s Law, Introduction Gauss’s law is an expression of the general relationship between the net electric flux
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This note was uploaded on 05/22/2010 for the course PHYS 2326 taught by Professor Staff during the Summer '08 term at HCCS.

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Physics for Scientists and Engineers 8ed - ch24 - PowerPoint Slides

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