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# lecture03 - 4 Gauss’s law 4.1 Electric flux Definition...

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Unformatted text preview: 4. Gauss’s law 4.1 Electric flux Definition: • Uniform electric field N N A N E N ~ cos ~ ~ ~ Φ θ θ A E EA A E EA E = = = = Φ ⊥ ⊥ θ cos • Not uniform electric field Perpendicular to the area E E - number of electric field lines N A area [ ] Vm C Nm E = = Φ 2 Units: A d E dA E d E = = Φ θ cos ∫ ∫ ∫ = = Φ = Φ A d E dA E d E E θ cos dA A ⇒ Example: Flux through open surface Compare the electric flux through two squares of areas A 1 and A 2 ( A 2 > A 1 ) placed in a region with a uniform electric field E : A. Φ 1 < Φ 2 B. Φ 1 = Φ 2 C. Φ 1 > Φ 2 A 1 (Side view ) The number of lines going through them is the same. The effective area for the large square is A 2cos θ = A 1 A 2 θ E θ A 2 cos θ • If you reverse the direction of A, you reverse the sign of the flux • For an open surface , choose any direction • For a closed surface it is conventional to take the area vector pointing outwards Ф > 0 ⇒ lines going out Ф < 0 ⇒ lines coming in Ф = 0 ⇒ no lines or a balance between incoming and outgoing lines A 2 E E The net flux is zero in both cases! Every line that comes in, goes out....
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lecture03 - 4 Gauss’s law 4.1 Electric flux Definition...

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