NOTES5 - 3/26/03 Dielectrics in an Electric Field...

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3/26/03 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 displaces the apparent charge centers of the atomic nucleus and surrounding spherical electron cloud relative to one another. E E - + + q - q d + - pd = q Relative displacement d of charge centers of electron cloud ( q ) and nucleus ( q ) in an applied electric field result in a net dipole moment p E d = q . Note d points towards q + . Spherical electron cloud and nucleus with no applied electric field. The relative displacement vector of the apparent charge centers times the amount of charge displaced is called the dipole moment, p d q d = q . A dipole produces a field that largely opposes the locally applied electric field, so that the average over a large collection of dipoles comprising a material under the influence of an applied electric field reduces the average field strength (i.e., the force on a unit test charge) over the material. 1 + 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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The net effect is related to the local dipole moment or polarization density P , defined as P pd == ∑∑ i i N ii i N V q V 11 where the index i corresponds to the i th dipole (pair of charges) and N is the number of dipoles in a small volume . If the polarization density varies with position, then an equivalent volume polarization charge density results. For example, the figure below illustrates a linearly varying dipole moment density P , resulting in a constant volume polarization charge density V ρ vp . Bound surface charge layer sp + + + + + + + + + + y Dielectric interface + Dipole pair x P 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. 2
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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 08/05/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

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NOTES5 - 3/26/03 Dielectrics in an Electric Field...

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