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(33) Electric Flux and Gauss's Law

# (33) Electric Flux and Gauss's Law - Lecture 33 Electric...

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Lecture 33 Electric Flux Gauss ’s Law

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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

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Electric Flux Φ Φ Φ = r r 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 = = ef f ect ive EA Φ = Line density is proportional to the magnitude of the electric field: cos θ = E A = r r
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 > A 1 ). A 2 A 1 (Side view) E (Front view of rectangles) A 1 A 2

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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 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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ACT: Flux through closed surface I A cubic box is placed in a region of uniform electric field as shown in figure 1.
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(33) Electric Flux and Gauss's Law - Lecture 33 Electric...

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