Electricity and MagnetismGauss’ LawElectric Flux‘Flux’ of water‘Flux’ of waterElectric FluxElectric FluxElectric FluxElectric FluxGauss’ LawGauss’ LawGauss’ LawExampleExampleExampleExample IIExample IIaExample IIIFeb 19 2002Electricity and Magnetism• Last time: Electric Field•Today: – Electric Flux– Gauss’ LawFeb 19 2002Gauss’ Law• Today: Gauss’ Law– Not so many demos, some math• Electricity and Magnetism in 4 equations: (1830)Feb 19 2002Electric Flux• Definition (simple case):• What does that mean?– Analogy with flow of e.g. waterElectric Flux ΦE= E AFeb 19 2002‘Flux’ of waterArea AVelocity vFlow: dV/dt = A dx/dt = AvFeb 19 2002‘Flux’ of waterArea AαVelocity vFlow: Av cos(α) = A vFeb 19 2002Electric Flux• Electric Flux: ΦE= E A• Same mathematical form as water flow• But there is no ‘substance’ flowing• Took almost a century to accept• Flux tells us how much field ‘passes’ through surface AFeb 19 2002Electric Flux• For ‘complicated’ surfaces:–Use integral• Often, ‘closed’ surfacesFeb 19 2002Electric Flux• Example of closed surface: Box• Flux in (left) = -Flux out (right): ΦE= 0• No ‘source’ of flux in this boxdAdAEFeb 19 2002Electric Flux• How to make ΦE non-zero?• Remember:• Put Charge Q inside ‘box’!+QFeb 19 2002Gauss’ Law• How are flux and charge connected?•Charge Qenclas source of flux through closed surfaceFeb 19 2002Gauss’ Law• Gauss vs Coulomb+QFeb 19 2002Gauss’ LawdA+Q• Gauss vs CoulombFeb 19 2002Example• Solid charged sphere (non-conducting)++++++++++++++++++++++A1r0Feb 19 2002Example• Solid charged sphere (non-conducting)++++++++++++++++++++++r0A2Feb 19 2002Example• Solid charged sphere (non-conducting)++++++++++++++++++++++r0ErE~rE~1/r2r0Feb 19 2002Example II• Conducting Sphere+++++++++++++++++ErE~1/r2r0E=0E=0Feb 19 2002Example IIa• Conducting Sphere+++++++++++++++++Feb 19 2002Example III• Line of Chargeλ: Charge density dQ/dll++++++
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