325_Sp2011_5_Conductors

325_Sp2011_5_Conductors - Electric Field Flux Gausss Law...

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin Electric Field Flux, Gauss’s Law, Divergence 1 5. Conductors EE325 Mikhail Belkin

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin Electric Field Flux, Gauss’s Law, Divergence 2 Current and current density When you apply electric field in a materials with mobile carriers, carriers start to move. Current is defined as charge flown per unit time: I= Q/ t (units [A] or [Coul/sec]) Current density J is current per area (units [A/m 2 ]) Current trough area S (normal to current density) is: I=J S Net current trough are S is: Charge conservation and current continuity charge is conserved (the sum of all charges in the universe is zero) For a area enclosed by surface S we have: = S S d J I = = - S S d J I dt dQ ) ( J dt d v = - ρ or Current continuity equation in integral and differential form
© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin Electric Field Flux, Gauss’s Law, Divergence 3 Charged particles in materials charge transport in “conductors” “real” particles are the carrier of current in a normal metal, the carrier is the electron electrons and holes in a solid respond to an electric field almost as if they were free particles in a vacuum, but with a different mass ordinary mass of an electron m e :9.11×10 -31 kg effective mass ( m *) helps capture the fact that the carrier is not really in “free space” consider a point charge in an “external” electric field electrons accelerate in response to the force velocity would continue to increase the longer the charge stays in the field just like falling in a gravitational field… electric field e - acceleration

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© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin Electric Field Flux, Gauss’s Law, Divergence 4 Scattering and “drift velocity” for us, let’s assume that throughout the material there are “scattering centers” (they act like air friction in free fall) on average the electron will travel for a time τ before it scatters electrons “collide” with scatterers, randomizing their velocities this leads to an overall average velocity that does NOT increase without bound in a constant force field (as a “free” particle would) we can calculate the “drift velocity” from the characteristic scattering time τ : consider an electron starting at rest in a constant electric field E the force on the electron is q e E acceleration is constant (Newton’s Second Law: F=ma) { * e force q E m a = * e q E a m =
© Copyright Dean P. Neikirk 2004-2009 Mikhail Belkin, EE 325, ECE Dept., UT Austin Electric Field Flux, Gauss’s Law, Divergence 5 Drift velocity and the scattering time assume that during the time τ the particle is in free-flight in the electric force field E, so at the end of time τ the velocity is assume that after the time interval τ the scattering event

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325_Sp2011_5_Conductors - Electric Field Flux Gausss Law...

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