Lect_33 - Flux in General DEMO Loop Lecture 33 Electric...

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Lecture 33 Electric Flux Gauss’s Law Flux in General Flux in General Max. flux Flux = 0 Less flux Flux: How much of something is passing through a surface. Flux depends on: The flow of the water The area of the tennis racquet A . How many hairs are passing through your scalp. If you dip a tennis racquet in a river, how much water flows through it? The orientation ( θ ) Effective area A A cos θ 0 θ DEMO: Loop Area vector A A A A θ Is a vector with: Magnitude: Area of surface Direction: Perpendicular to surface Electric Flux Φ Φ = G G E da In general (for any field and surface): Instead of water, we have electric field lines. How many lines go through a given surface? For uniform E and flat surfaces only 2 [ ] Nm /C Vm Φ = = effective EA Φ = Line density is proportional to the magnitude of the electric field: cos EA θ = E A = G G

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ACT: Flux through open surface ACT: Flux through open surface Two rectangles with one identical side (perpendicular to the screen in the side view) and one different side are placed in a region with a uniform electric field E. The areas of the rectangles are A 1 and A 2 ( A 2 > A 1 ). A 2 A 1 (Side view) E (Front view of rectangles) A 1 A 2 Compare the electric flux through the two rectangles: A. Φ 1 < Φ 2 B. Φ 1 = Φ 2 C. Φ 1 > Φ 2 A 2 A 1 (Side view) The number of lines going through them is the same. A 2 θ E θ A 2 cos θ The effective area for the large square is A 2 cos θ = A 1 Sign matters! If you reverse the direction of A, you reverse the sign of the flux • For an open surface, choose any direction as long as the choice is made clear • For a closed surface , the convention is to take the area vector pointing outwards Flux > 0 lines going out Flux < 0 lines coming in Flux = 0 no lines or a balance between incoming and outgoing lines.
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