lecture7 - Lecture 7 Polarization In this lecture you will...

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1 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Lecture 7 Polarization In this lecture you will learn: • Material Polarization • Mathematics of Polarization • Dielectric Permittivity • Conductors Vs Dielectrics • Appendix ECE 303 – Fall 2007 – Farhan Rana – Cornell University Charge Dipoles and Dipole Moments Consider a charge dipole: d r q q + Dipole moment of the charge dipole is a vector such that: p r d q p r r =
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2 ECE 303 – Fall 2007 – Farhan Rana – Cornell University V +- φ = V = 0 + + + + + + + + - - - - - - - - V = V = 0 + + + + + + + + - - - - - - - - + + + + + + + + - - - - - - - - Conductors in Electric Fields – A Review • Consider the problem when a conductive plate was placed inside an electric field • Conductors have “free charges” that are able to move around (mostly these “free charges” are electrons that are not attached to any particular atom) • Under the influence of external E-field these free charges move to completely screen out the E-field from within the conducting material +ve nucleus + -ve sea of free electrons Conductors Sea of Free Electrons +++ σ ECE 303 – Fall 2007 – Farhan Rana – Cornell University Dielectrics in Electric Fields - Polarization Many materials do not have “free electrons” that can move around, but have electrons bound to atoms, as shown below + +ve nucleus + + + + + + + + + + + + + + + + + + -ve electron cloud + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - Dielectric in an E-field In the presence of an E-field, the electron cloud in each atom distorts ALMOST INSTANTANEOUSLY so that each atom looks like a charge dipole Dielectric E
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3 ECE 303 – Fall 2007 – Farhan Rana – Cornell University + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - Dielectrics in Electric Fields – Polarization Vector The polarization vector is a vector such that: P r + - = dipole moment of each dipole d r d Q p r r = d NQ p N P v r r = = Where N is the number of charge dipoles per unit volume in the material The units of are: Coumlombs/m 2 P r The polarization vector characterizes the polarization density of the medium under the influence of the electric field P r + Q - Q E ECE 303 – Fall 2007 – Farhan Rana – Cornell University Dielectrics in Electric Fields – Electrical Susceptibility + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - Naturally, one would expect the polarization of the material to be proportional to the strength of the electric field: E P E P e o r r r r χ ε = The constant of proportionality e is called the electrical susceptibility of the material E
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4 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Material Polarization and Surface Charge Densities + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + - - - - - - - - - - - - • The stuff inside the box in on the average charge neutral (same number of positive and negative charges)
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lecture7 - Lecture 7 Polarization In this lecture you will...

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