Gauss Law (1) - cancel each other out and that is why the...

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Flux and Gauss' Law Ch 22 AP Physics C
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Background Gauss’ Law is part of the key to using symmetry considerations to simplify E- Field calculations (remember section 21.5 when we integrated to solve for E of a ring of charge, line of charge etc.) In chapter 21 we asked: What is the E-field due to a known charge distribution? In chapter 22 we will ask: What is the charge distribution if we know E ?
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The box may enclose a charge, by placing a test charge and observing F, we know E. It is only necessary to do this at the surface of the shape.
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Flux Flux, in this case Electric Flux, is the amount of (electric) field passing through a specified area. Think of water flowing in a pipe (flux comes from the Latin for “flow”)
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Pictures of outward (+) flux and inward (-) flux
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Situations where the total flux equals zero
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The E-field decreases at 1/r 2 while the area increases at r 2 and that increase and decrease
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Unformatted text preview: cancel each other out and that is why the size of the surface enclosing Q does not matter. Flux • Symbol Ф E • Unit Nm 2 /C • Equation: ∫ ⋅ = Φ = ⋅ = Φ A d E EA A E E E θ cos What we can conclude about Ф 1. Ф is proportional to q 2. Whether Ф is inward or outward depends on the q inside the surface 3. A q outside the surface offers zero Ф because Ф in = Ф out Ф = 0 through triangular prism below. See board for the proof E = 500 N/C 40 cm 50 cm 30 cm 40 cm Gauss’ Law • The total electric flux through any closed surface is proportional to the net electric charge inside the surface Gauss’ Law cos ε θ enclosed enclosed E Q dA E dA E A d E Q A d E = = = ⋅ = ⋅ = Φ ∫ ∫ ∫ ∫ ⊥ Point Charge Uniformly charge insulator at a varying r Line of Charge Sheet of Charge...
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