4 2 Dielectrics Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jo[.]
Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India 4.2 Dielectrics 4.2-3 Dielectrics are based upon the property of polarization, which is the phenomenon of the creation of electric dipoles within the material Electronic polarization: (bound electrons are displaced to form a dipole) E + - Q + d -Q - Dipole moment p = Qd 4.2-4 Orientational polarization: (Already existing dipoles are acted upon by a torque) QE + q d q - E Torque QEd sin Direction into the paper T Qd × E p × E - QE Ionic polarization: (separation of positive and negative ions in molecules) 4.2-5 The phenomenon of polarization results in a polarization charge in the material which produces a secondary E - rS0 z=d - - - - - - - + + + - Ea e e z=0 + + + + rS0 z=d z=0 + - + - + + - + + + - + pS pS + + + + - + + + - + ES - pS pS + - + + - + + + - t + + E+ + + 4.2-6 Polarization Current 4.2-7 To take into account the effect of polarization, we define the displacement flux density vector, D, as D 0E P = E e E = 1 e E = 0 r E = E C m2 = permittivity, F m r = relative permittivity r and vary with the material, implicitly taking into account the effect of polarization 4.2-8 As an example, consider S - - - - - - - z=d z + + + + S + Then, inside the material, + + z=0 S S E az a z 2 2 S az D E S a z 4.2-9 D4.3 1 C m2 - - - - - - - z=d z 4 + + + + + + 1 C m2 For < z < d, 6 (a) D S 0az 10 a z C m + z=0 4.2-10 D 6 (b) E 10 az 4 36 6 10 az 9 10 9000 az V m (c) P D E = 10 az 0.25 10 az 0.75 10 az C m2 4.2-11 Isotropic Dielectrics: D is parallel to E for all E y Dx Ex D Dy Ey Dz Ez D E E x Anisotropic Dielectrics: D is not parallel to E in general Only for certain directions (or polarizations) of E is D parallel to E These are known as characteristic polarizations 4.2-12 Dx xx Ex xy Ey xz Ez Dy yx Ex yy Ey yz Ez Dz zx Ex zy Ey zz Ez y E D x Dx xx D y yx Dz zx xy xz Ex yy yz Ey zy zz Ez 4.2-13 D4.4 0 0 0 (a) E E0 az Dx 0 D 0 0 y Dz 0 E0 9 D 9 E0 az 9 E eff 9 , reff 4.2-14 (b) E E0 a x 2a y Dx E0 E0 0 E 8E D 0 0 y Dz 0 D 4 E0 ax 2a y 4 E eff 4 , reff 4.2-15 (c) E E0 2ax a y Dx E0 18 E0 D 0 E E 0 y 0 Dz 0 D 9 E0 2ax a y 9 E eff 9 , reff