gauss law - GAUSS LAW ELECRIC FLUX Dr Manjunatha S Plasma...

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GAUSS LAW ELECRIC FLUX Dr Manjunatha S
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Plasma ball, the colorful lines emanating from the sphere give evidence of strong electric field. 2 Dr MANJUNATHA S, CS&IS
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Karl Friedrich Gauss (1777-1855) – German mathematician Gauss’s Law Gauss’s Law 3 Dr MANJUNATHA S, CS&IS
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Karl Friedrich Gauss (1777-1855) – German mathematician Already can calculate the E-field of an arbitrary charge distribution using Coulomb’s Law. Gauss’s Law allows the same thing, but much more easily… … so long as the charge distribution is highly symmetrical . Gauss’s Law Gauss’s Law 4 Dr MANJUNATHA S, CS&IS
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Electric Flux Electric Flux Measures how much an electric field wants to “push through” or “flow through” some arbitrary surface area Definition : The total no of lines of force emanation from a charge. Denoted by a Greek letter Φ Flux lines Plane Area Dr MANJUNATHA S, CS&IS
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Electric Flux: E-Flux through a surface depends on three things: 1. How strong the E-field is at each infinitesimal area. 2. How big the overall area A is after integration. 3. The orientation between the E-field and each infinitesimal area. 6 General Equation for Electric Flux is Dr MANJUNATHA S, CS&IS
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Easiest case : The E-field is uniform The plane is perpendicular to the field Electric Flux Electric Flux – Case 1 – Case 1 Electric Flux 7 Dr MANJUNATHA S, CS&IS
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Easiest case : The E-field is uniform The plane is perpendicular to the field Electric Flux Electric Flux – Case 1 – Case 1 Electric Flux Flux depends on how strong the E-field is and how big the area is. 8 Dr MANJUNATHA S, CS&IS
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Electric Flux We have used electric field lines to visualize electric fields and indicate their strength. We are now going to count* the number of electric field lines passing through a surface, and use this count to determine the electric field. E *There are 3 kinds of people in this world: those who can count, and those who can’t. 9 Dr MANJUNATHA S, CS&IS
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The electric flux passing through a surface is the number of electric field lines that pass through it. Because electric field lines are drawn arbitrarily, we quantify electric flux like this: E =E . A, except that… If the surface is tilted, fewer lines cut the surface . E A Later we’ll learn about magnetic flux, which is why I will use the subscript E on electric flux. E The green lines miss! 10 Dr MANJUNATHA S, CS&IS
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E A The “amount of surface” perpendicular to the electric field is A cos . A Effective = A cos so E = EA Effective = EA cos . We define A to be a vector having a magnitude equal to the area of the surface, in a direction normal to the surface. Therefore, the amount of surface area effectively “cut through” by the electric field is A cos . Remember the dot product , E E A r r 11 Dr MANJUNATHA S, CS&IS
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If the electric field is not uniform, or the surface is not flat… divide the surface into infinitesimal surface elements and add the flux through each… E i E i i A 0 i lim E A  r r E E dA
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