lecture5 - For a closed surface S: take the outward...

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Gauss’s Law •Electric Flux •Gauss’s Law •Examples Text 24.1—24.2 Practice Problems: Chapter 24, problems 1, 5, 6, 11, 15, 21 Gauss’s Law (Chapter 24) Gauss’s Law (Chapter 24) What’s in the box ??
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Electric Flux Electric Flux Φ E the “number of field lines through a surface S ” For uniform , define : E r = Φ A E E r where is the “area perpendicular to A . r S θ (Units: N•m 2 /C) n ˆ φ cos A so. .. sin A : Note = = E Notes: Notes: 1) Φ E is a scalar . 2) Units: N•m 2 /C 3) Φ E is a quantitative measure of “the number of field lines through S.” 4) Φ E refers to flux through some particular surface S.”
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n ˆ Unit vector surface (“unit normal”) Area A Define “area vector” : n A ˆ ) ( = area r A r A Then for uniform E, A E EA r r = = Φ θ cos area | | = A r rface) ular to su (perpendic ˆ || n A r Examples: Examples: Find: flux through S 1 , S 2 , S 3 . Φ C N 1000 = r 30° (rectangle, 1m x 2m) (rectangle, 1m x 2m) (hemisphere, radius 1m) S 2 S 1 S 3
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If E is not uniform, or S is not flat, then: For a small surface , dA dA E = E d Φ For the whole surface, = S E Φ dA E dA E S cos θ = r Gauss’s Law Gauss’s Law
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Unformatted text preview: For a closed surface S: take the outward direction as the positive direction for ; then A d n r , Total flux through S enclosed charge net = 2 2 C N m vacuum" of ty permittivi " = 12 10 85 . 8 e e k k 4 1 , 4 1 and = = Example : point charge + r q E S: sphere, radius r, centred on the charge. dA E E Example: + centred + outside + near edge Example: Example: +Q-2Q +3Q S 1 S 2 S 3 S 1 , S 2 , and S 3 represent closed 3-dimensional surfaces. Find the total electric flux through each surface. To prepare for next the lecture To prepare for next the lecture , , review geometry, and answer: review geometry, and answer: What is a) The volume of a sphere of radius r? b) The surface area of a sphere of radius r? c) The volume of the cylinder? d) The total surface area of the cylinder? L r...
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This note was uploaded on 12/03/2009 for the course CHEMISTRY 1E03 taught by Professor Britz during the Spring '09 term at McMaster University.

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lecture5 - For a closed surface S: take the outward...

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