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Darryl Michael/GE CRD Fields and Waves Lesson 3.4 ELECTROSTATICS - MATERIALS
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CONDUCTORS and DIELECTRICS ConductorsDielectrics High conductivities; (for Copper) ~ 5.8x10 7 S/m Low conductivities; (for Rubber) ~ 1x10 -15 S/m or 1/ -m Semiconductors (mid ’s) Permittivities, = 1-100 Note: 0 is the permittivity of free space/vacuum = 8.854 x 10 -12 F/m
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CONDUCTORS Lattice of Nuclei Most electrons are stuck to the nucleus But, 1 or 2 electrons per atom are free to move This means that if you apply an external E- field, the free electrons will move
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CONDUCTORS - - - - - - - - - - + + + + + + + + + + Apply external E-field, electrons conductor Force on electrons causes free electrons to move Charge displacement causes response E-field (opposite to applied external E-field)
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CONDUCTORS The electrons keep moving until, This means that:, in a conductor Conductor is equipotential Do problem 1
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DIELECTRICS + + electron cloud nucleus electron cloud centered on nucleus Cloud shifts to setup
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DIELECTRICS Define: dipole moment Polarizationpartially cancels applied Field
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DIELECTRICS Define: Displacement Flux Density ( C/m 2 ) Electric Field (V/m) subtracts out bound charge is due to bound/dielectric charge and free charge is due to bound/dielectric charge only and opposite sign is due to free charge only
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FREE CHARGES Examples of free charges: s on conductor electron beam doped region of semi-conductor Gauss’ Law uses just free charge Most general form
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DIELECTRICS Don’t need to know about bound charges to findMany materials have Define, where Typically, Do Problem 2
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DIELECTRIC BREAKDOWN - part d of problem Example: Arc in Air If E-field is too large, it will pull electrons off from atom These electrons are accelerated by the E-field These accelerated electrons then collide with more atoms that knock off more electrons This is an AVALANCHE PROCESS BREAKDOWN OCCURS if Damages materials - there is a Voltage limit on components, cables in air : = 30 kV/cm
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BOUNDARY CONDITIONS - Normal Components all derived from Maxwell’s equations NORMAL COMPONENT h a Gaussian Surface Material 1 Material 2 Take h << a (a thin disc) TOP BOTTOM
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Case 1: REGION 2 is a CONDUCTOR, D 2 = E 2 =0 Case 2: REGIONS 1 & 2 are DIELECTRICS with s = 0 Can only really get s with conductors BOUNDARY CONDITIONS - Normal Components
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BOUNDARY CONDITIONS - Tangential Components Material 1 Material 2 w h h << w If region 2 is a conductor E 1t = 0 Note: Outside conductor E and D are normal to the surface
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