Lect06Polarizable - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 6 2009/9/9 Polarization of Materials Mathematics of Polarization Dielectric Permittivity + + + + - 1 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: Instructor: Dr. Wesley E. Swartz Conductors versus Dielectrics Capacitance + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - V + - + + ++++++++ + + + + - - - - ---- - -- - - - Charge Dipoles and Dipole Moments Consider a charge dipole: d q q + 2 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: The dipole moment of the charge dipole is a vector such that Note that the vector points from the negative charge to the positive charge! p d q p = d Conductors in Electric Fields – A Review Consider the problem where 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 an external E-field these free charges move to completely screen out the E-field from within the conducting material V +- φ = V = 0 + + + + + + + + - - - - - - - - 3 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: conducting material. V = V = 0 + + + + + + + + - - - - - - - - + + + + + + + + - - - - - - - - +ve nucleus + -ve sea of free electrons Conductors with a Sea of Free Electrons +++ σ Dielectrics in Electric Fields (1) 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 Dielectric with no applied E E 4 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: 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 . + + + + + + + + + + + + + + + + + + - - - - - - - - - Now define the polarization vector to be where N is the number of charge dipoles per unit volume in the material. The units of are: Coumlombs/m 2 The polarization vector characterizes the polarization of the medium under the Dielectrics in Electric Fields (2) Take the dipole moment of each molecule to be . + + + - - - P + - d d Q p = N p P = P P + Q - Q E 5 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: polarization of the medium under the influence of an electric field. Naturally, one would expect the polarization of the material to be proportional to the strength of the electric field: The constant of proportionality is called the electrical susceptibility of the material. E P E P e o χ ε = + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - e Material Polarization and Surface Charges + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - + + + + + + + + + + - - - - - - - - - - P p = P p + = E 6 Swartz and Rana 06/5/23 Electromagnetic Fields and Waves – Fall 2009 Lecture 6: The stuff inside the dashed line box is on the average charge neutral (same number of positive and negative charges.
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Lect06Polarizable - ECE 3030 Electromagnetic Fields and...

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