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# Fields and Waves

Fields and Waves. Lesson 3.4. ELECTROSTATICS - MATERIALS. CONDUCTORS and DIELECTRICS. Conductors. Dielectrics. High conductivities; s (for Copper) ~ 5.8x10 7 S/m. Low conductivities; s (for Rubber) ~ 1x10 -15 S/m or 1/ W -m. Semiconductors (mid s ’s).

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## Fields and Waves

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1. Fields and Waves Lesson 3.4 ELECTROSTATICS - MATERIALS Darryl Michael/GE CRD

2. CONDUCTORS and DIELECTRICS Conductors Dielectrics High conductivities; s (for Copper) ~ 5.8x107 S/m Low conductivities; s (for Rubber) ~ 1x10-15 S/m or 1/W-m Semiconductors (mid s’s) Permittivities, e = 1-100e0 Note: e0 is the permittivity of free space/vacuum = 8.854 x 10-12 F/m

3. CONDUCTORS 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 Lattice of Nuclei

4. - - + + + + - - - - + + - - + + - - + + CONDUCTORS conductor electrons Apply external E-field, • Force on electrons causes free electrons to move • Charge displacement causes response E-field (opposite to applied external E-field)

5. , in a conductor Conductor is equipotential CONDUCTORS The electrons keep moving until, This means that: Do problem 1

6. + + DIELECTRICS electron cloud nucleus electron cloud centered on nucleus Cloud shifts to setup

7. Define: dipole moment Polarization partially cancels applied Field DIELECTRICS

8. DIELECTRICS subtracts out bound charge Define: Displacement Flux Density ( C/m2 ) Electric Field (V/m) 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

9. FREE CHARGES Examples of free charges: rs on conductor electron beam doped region of semi-conductor Gauss’ Law uses just free charge Most general form

10. Don’t need to know about bound charges to find Many materials have Define , where Typically, DIELECTRICS Do Problem 2

11. Damages materials - there is a Voltage limit on components, cables in air : = 30 kV/cm 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

12. BOUNDARY CONDITIONS - Normal Components • all derived from Maxwell’s equations NORMAL COMPONENT Take h << a (a thin disc) a Material 1 TOP h Material 2 BOTTOM Gaussian Surface

13. BOUNDARY CONDITIONS - Normal Components REGION 2 is a CONDUCTOR, D2 = E2 =0 Case 1: Case 2: REGIONS 1 & 2 are DIELECTRICS with rs = 0 Can only really get rs with conductors

14. BOUNDARY CONDITIONS - Tangential Components w Material 1 h << w h Material 2 If region 2 is a conductor E1t = 0 Note: Outside conductor E and D are normal to the surface

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