PHY132_L04 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 4 Gauss’ Law Lecture 4 1 02/01/2010
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Electric Flux The electric flux measures the “amount of electric field” E that “crosses” a surface A : A E E E E A θ θ =90º small angle 90º angle large flux zero flux • Definition: • Generally, for a CURVED surface nd a NON niform field: cos E EA θ Φ≡ = EA and a NON-uniform field: cos Ei i i i i ii dE A = Δ = Δ E A θ i 02/01/2010 Lecture 4 2
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Gauss’ Law states: A. encl. 0 surface dQ ε ⋅= EA v A B. C. both A and B encl. 0 Q . th an 02/01/2010 Lecture 4 3
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Gauss’ Law For CLOSED curved surfaces the total flux must be zero – if field lines do not start or disappear inside the enclosed volume … –ve ry similar to the flow theorem of incompressible fluid: what goes in must come out … – in formula form: if surface encloses no net charge !! urface 0 E d Φ ≡⋅ = EA v Generally, IF net charge Q encl is enclosed: Surface cl Q E ¾ Gauss’ Law encl 0 Surface E d ε Φ = v d A r Simple example: 2 encl 00 urface ()4 Q d Q Er r π ⋅= = = A E v 02/01/2010 Lecture 4 4 Surface 2 0 1 () 4 Q r πε ⇒=
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Gauss’ Law Field of a point charge Q: Gaussian surface encl 0 Surface E Q d ε Φ ≡⋅ = EA v Gaussian surface E ( r ) r E ( r ) r y Q Q x auss’ Law works for both surfaces (or for any other) Gauss Law works for both surfaces (or for any other)
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This note was uploaded on 04/14/2010 for the course PHY 132 taught by Professor Rijssenbeek during the Spring '04 term at SUNY Stony Brook.

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PHY132_L04 - Classical Physics II Classical Physics II...

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