2049_ch23A - Chapter 23 Gauss Law PHY2049 Chapter 23 1 Two...

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PHY2049: Chapter 23 1 Chapter 23: Gauss’ Law
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PHY2049: Chapter 23 2 Coulomb’s Law Gauss’ Law Derivation given in Sec. 23-5 (Read!) Not derived in this book (Requires vector calculus) equivalent We will focus on what is Gauss’ law and how we use it. Two Equivalent Laws for Electricity
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PHY2049: Chapter 23 3 Electric Flux Î Simple definition of electric flux (E constant, flat surface) ± E at an angle θ to planar surface, area A ± Units = N m 2 / C (SI units) Î Simple example ± Let E = 10 4 N/C pass through 2m x 5m rectangle, 30 ° to normal ± φ E = 10 4 * 10 * cos(30 ° ) = 100,000 * 0.866 = 86,600 Î More general Φ E definition (E variable, curved surface) cos E EA θ Φ≡ = EA E S d Normal E
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PHY2049: Chapter 23 4 Example of Constant Field N/C ˆ 4 i = E 2 m ) ˆ 3 ˆ 2 ( j i + = A C / Nm 8 ) ˆ 3 ˆ 2 ( ˆ 4 Φ 2 = + = j i i E A E
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PHY2049: Chapter 23 5 Flux Through Closed Surface Î Surface elements dA always point outward! Î Sign of Φ E ± E outward (+) ± E inward ( ) Φ E < 0 Φ E = 0 Φ E > 0
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PHY2049: Chapter 23 6 Example: Flux Through Cube Î E field is constant: ± Flux through front face? ± Flux through back face?
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2049_ch23A - Chapter 23 Gauss Law PHY2049 Chapter 23 1 Two...

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