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1 Dielectrics in an Electric Field Conductors are characterized by the fact that a large number of free charges are available which move almost instantaneously in the presence of an applied electric field. By contrast, dielectrics are characterized by the electrical effects produced by their bound charges. These effects result from the separation of charges bound to the nuclei of atomic molecules comprising the material. As illustrated in the figure below, a simple model suggests that the force on atomic charges resulting from an applied field E will displace the apparent center of the spherical electron cloud of an atomic nucleus relative to the nucleus. The relative vector displacement d of the apparent charge centers times the amount of charge q displaced is called the dipole moment, pd = q . A dipole produces a field that largely opposes locally the applied electric field, so that a large collection of dipoles comprising a material under the influence of an applied electric field reduces the field strength (i.e., the force on a unit test charge) over most regions of the material. This set of notes is related to the material in Sections 3.6-3.10 in the text by D.K. Cheng. 3/08/00 - + Spherical electron cloud and nucleus with no applied electric field. + - E + - E d q q = q Relative displacement d of charge centers of electron cloud ( q ) and nucleus ( q ) in an applied electric field E result in a net dipole moment = q . + E dipole E An electric field opposing the applied electric field exists in the vicinity of a dipole. + + + + + + An ensemble of dipole moments within a dielectric material opposes the applied electric field and reduces, on average, the strength of the total field (force on a unit test charge). E

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2 The dipole moment or polarization density P within a small volume Δ V is defined as P pd == ∑∑ i i N ii i N V q V 11 Δ Δ where the index i corresponds to the i th dipole (pair of charges) and N is the number of dipoles in Δ V . If the polarization density varies with position, then an equivalent volume polarization charge density can result. For example, the figure below illustrates a linearly varying dipole moment density P resulting in a constant volume polarization charge density ρ vp . + + + + + + + + + + + Dipole density P increasing linearly in x results in a net negative, volume polarization charge density vp within dashed volumes interior to the dielectric. A layer of bound surface polarization charge density sp results at the dielectric interface. x y Dielectric interface Bound surface charge layer sp P Dipole pair
3 A detailed analysis shows that, in general, The bound or polarization volume charge density resulting from a varying dipole moment density is given by ρ vp = − ∇⋅ P .

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## This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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notes5 - This set of notes is related to the material in...

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