This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 8 Conductors, dielectrics, and polarization So far in this course we have examined static field configurations of charge distributions assumed to be fixed in free space in the absence of nearby materials (solid, liquid, or gas) composed of neutral atoms and molecules. In the presence of material bodies composed of large number of charge- neutral atoms (in fluid or solid states) static charge distributions giving rise to electrostatic fields can be typically 1 found: + + + + + + + + + +- - - - - - - - - - (a) E o = ˆ z ρ s o + + + + + + + + + +- - - - - - - - - - (b) E o E o- ρ s ρ s- ρ s ρ s- ρ s ρ s- - - - - - - - - - + + + + + + + + + + σ > E = 0 A conducting slab inserted into a region with field E_o (as shown in b)develops surface charge which cancels out E_o within the slab. E_o relates to surface charge as dictated by Gauss’s law and superposition principle. 1. On exterior surfaces of conductors in “steady-state”, 2. In crystal lattices occupied by ionized atoms, as in depletion regions of semiconductor junctions in diodes and transistors. In this lecture we will examine these configurations and response of materials to applied electric fields. Conductivity and static charges on conductor surfaces: • Conductivity σ is an emergent property of materials bodies con- taining free charge carriers (e.g., unbound electrons, ionized atoms or molecules) which relates the applied electric field E (V/m) to the elec- trical current density J (A/m 2 ) conducted in the material via a linear 1 More generally, materials containing charge carriers exhibiting divergence free flows will also exhibit static charge distributions. 1 relation 2 J = σ E . ( Ohm’s Law) • Simple physics-based models for σ will be discussed later in Lecture 11. For now it is sufficient to note that: – σ → ∞ corresponds to a perfect electrical conductor 3 (PEC) for which it is necessary that E = 0 (in analogy with V = 0 across a short circuit element) independent of J . – σ → corresponds to a perfect insulator for which it is necessary that J = 0 (in analogy with I = 0 through an open circuit element) independent of E . • While (macroscopic) E = 0 in PEC’s unconditionally , a conductor with a finite σ (e.g., copper or sea water) will also have E = 0 in “steady- state” after the decay of transient currents J that may be initiated within the conductor after applying an external electric field E o (see margin). + + + + + + + + + +- - - - - - - - - - (a) E o = ˆ z ρ s o + + + + + + + + + +- - - - - - - - - - (b) E o E o- ρ s ρ s- ρ s ρ s- ρ s ρ s- - - - - - - - - - + + + + + + + + + + σ > E = 0 A conducting slab inserted into a region with field E_o (as shown in b)develops surface charge which cancels out E_o within the slab....
View Full Document
- Spring '08
- Electric charge, Permittivity, Fundamental physics concepts, Dielectric