Ch4 - Electrostatic field in dielectric media • All...

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Unformatted text preview: Electrostatic field in dielectric media • All matters consist of charged constituents (i.e. electrons and nuclei) that can be displaced by an electric field. For e.g. : an electric dipole could be formed by applying an E-field on an originally symmetrical (i.e. zero dipole moment) atom. This dipole, in turn, would produce an electric field that affect the charge distribution of neighbouring atoms. • Inside a material, the E-field rapidly varies over a length scale corresponds to the spacing between the atoms or molecules. The problem would be hopelessly complicated if we insist in finding the E-field at every mathematical ‘point’. • If, instead, we are interested in the average value of the E-field over a finite volume, it is then something we can handle. This volume should be small enough to be practically regarded as a ‘point’, but yet big enough to contain enough atoms or molecules to give a smoothly varying average value. Ideal conductors : Supply unlimited freely moving charge in response to an E-field, with a net result to completely shield the E-field in the bulk of the conductor Dielectrics : The charges are bounded to an atom or molecule. In response to an E-field, the +ve and –ve charges will redistribute, and tends to shield the E-field, but the shielding would not be complete. The E-field inside the material would become smaller by this shielding effect. A dipole could be induced by the E-field from an atom or molecule with an originally zero dipole moment. Some molecules contain permanent dipole moment . In this case the permanent dipole would be aligned by the E-field. e.g. of molecules with permanent dipole moment : Let’s use a simple model to calculate the response of an atom to an external E-field : e.g. (Griffith Ex. 4.1) An atom can be modeled as an uniformly distributed charged sphere of radius a and total charge –q surrounding a point nucleus +q . In response to an external E- field, the +ve and –ve charges would be displaced apart from each other : Force on the nucleus by the electron cloud = qE electron = 3 a 4 qd q πε Force on the nucleus by the external field = qE ext In equilibrium, = 3 ext a 4 qd q qE πε ∴ ext 3 E q a 4 d πε = The dipole moment induced by the external field p = qd = ext ext 3 E E a 4 α πε ≡ where α is called the polarizability of the atom. • The induced dipole moment p of an atom or molecule is related to the local electric field by p = α E The polarizability α is a property that depends on the structure of an atom or molecule • For a medium that consists of a collection of many atoms or molecules, we can define an averaged quantity called the polarization P , which is the net dipole moment in a unit volume ....
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This note was uploaded on 10/14/2010 for the course PHYS 2051 taught by Professor Drkwong during the Spring '10 term at CUHK.

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Ch4 - Electrostatic field in dielectric media • All...

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