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Lecture04_Kim

# Lecture04_Kim - Lecture 4-1 Lecture 4-2 Gauss's Law...

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1/19/2012 1 Lecture 4-1 Gauss’s Law: Qualitative Statement (Review) square4 Form any closed surface around charges square4 Count the number of electric field lines coming through the surface, those outward as positive and inward as negative. square4 Then the net number of lines is proportional to the net charges enclosed in the surface . Lecture 4-2 Electric flux (Review) # of field lines N = density of field lines x “area” To state Gauss’s Law in a quantitative form, we first need to define Electric Flux. Surface can be of any shape Surface can be open or closed Must specify “which way” ɵ N E A E An = combarrowextenderharpoonrightnosp combarrowextenderharpoonrightnosp i ɵ E E An Φ combarrowextenderarrowrightnosp “area”=A = A × cos θ if A is tilted θ A Lecture 4-3 Electric flux through Arbitrary Surface General definition of electric flux: E S E ndA Φ = combarrowextenderharpoonrightnosp ɵ i (must specify sense , i.e., which way ) ɵ E E An Φ = combarrowextenderharpoonrightnosp i Divide the surface into many very small, nearly flat plaquettes and sum over the contributions from all of them. Lecture 4-4 Electric Flux through Closed Surface E n arrowrightnosp ɵ i E S E ndA Φ = combarrowextenderharpoonrightnosp ɵ i integralloop • This integral is over a CLOSED surface. • Since is a scalar product, the electric flux is a SCALAR quantity The integration element is a vector normal to the surface and points OUTWARD

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Lecture04_Kim - Lecture 4-1 Lecture 4-2 Gauss's Law...

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