Lecture 8 - 8 Conductors, dielectrics, and polarization •...

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Unformatted text preview: 8 Conductors, dielectrics, and polarization • We have so far been examining static field configurations of charge dis- tributions assumed to be fixed in free space, in the absence of materials (solid, liquid, or gas) composed of neutral atoms and molecules. • In practice free charge carriers can have static distributions when their motions (in response to the fields of other charge carriers) are prevented by contact forces of adjacent atoms or molecules (or have divergence- free motions to be examined in future lectures). A static charge distribution is possible under the following conditions: 1. On exterior surfaces of conducting solids: conductors are materi- als containing free charge carriers (e.g., electrons, ionized atoms or molecules) which are free to drift and conduct electric currents. • In steady-state a conductor will have zero internal electric field and zero current, and a static surface charge density ρ s that produces a static field that exactly cancels out externally imposed fields in the interior of the conductor (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. E_o relates to surface charge as dictated by Gauss’s law and superposition principle. • E = 0 in the interior at steady-state implies that potential V = const., as well as ρ = ∇· D = ∇· o E = 0 . – Surface charge density ρ s and the exterior field on a conductor surface will satisfy the boundary condition equations ˆ n · D = ρ s and ˆ n × E = 0 , 1 with ˆ n denoting the outward unit normal. – A transient (or time-varying) electric field E can exist within a conductor (before steady-state is reached), causing a current flow J = σ E , where σ is said to be the conductivity of the medium (discussed in more detail later on). Steady-state is reached when charge transport via J establishes a surface charge ρ s that just cancels the externally imposed fields within the conductor....
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This note was uploaded on 05/05/2010 for the course ECE ece 442 taught by Professor Kim during the Spring '10 term at University of Illinois at Urbana–Champaign.

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Lecture 8 - 8 Conductors, dielectrics, and polarization •...

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