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Electromagnetic Field Theory: A Problem Solving Approach Part 20. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Field Boundary Conditions 165 The potential in each region is 1 q q 1 Vll 2 J 2 2-11 2 y 0 4tT 2 A Z J with resultant electric field 1 qtxix O-dJij ziJ q txix Gi dlij ziJX 4TO1 x2 y d 2 z2 3 2 x2 y d 2 z2 3 2 7 En V Vi i 4 4ir 2 xU Cy-dlij zt x2 y d 2 z2 3 2 To satisfy the continuity of tangential electric field at y 0 we have E i Exn w w e 62 Eil E2ii 8 With no surface charge the normal component of D must be continuous at y 0 eiEyI e2E n -q q -q 9 Solving 8 and 9 for the unknown charges we find 2 E1 1 2 2e2 n 4 z l 2 10 The force on the point charge q is due only to the field from image charge _ 44 . fl2 2 1 . . 4t7 1 2C 21 _16rr 1 1 2 i 21 l 3 3-4 Normal Component of P and e0E By integrating the flux of polarization over the same Gaussian pillbox surface shown in Figure 3-12i we relate the discontinuity in normal component of polarization to the surface polarization charge density at using the relations 166 Polarization and Conduction from Section 3.1.2 P P dS - I atdS P2n Pin -Op n P2 - Pi -crp s Js 12 The minus sign in front of at results because of the minus sign relating the volume polarization charge density to the divergence of P. To summarize polarization charge is the source of P free charge is the source of D and the total charge is the source of EqE. Using 4 and 12 the electric field interfacial discontinuity is n-H F _n D2 Dl P2-Pl _ 7 0r n ISi ---------------------- ------- 15 Eo E0 For linear dielectrics it is often convenient to lump polarization effects into the permittivity e and never use the vector P only D and E. For permanently polarized materials it is usually convenient to replace the polarization P by the equivalent polarization volume charge density and surface charge density of 12 and solve for E using the coulombic superposition integral of Section 2.3.2. In many dielectric problems there is no volume polarization charge but at surfaces of discontinuity a surface polarization charge is present as given by 12 . EXAMPLE 3-2 CYLINDER .
