tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 73

Electromagnetic Field Theory: A Problem Solving Approach Part 73. 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. | Problems 695 which is plotted versus kL in Fig. 9-14. This result can be checked in the limit as L becomes very small kL 1 since the radiation resistance should approach that of a point dipole given in Section 9-2-5. In this short dipole limit the bracketed terms in 14 are lim t kL i sin kL kL 1 2 kL 6 i cos kL I-------- 15 kLSi kL kL 2 so that 14 reduces to . V kL hm R ---------- kL i 2tt 3 16 which agrees with the results in Section 9-2-5. Note that for large dipoles kL 1 the sine integral term dominates with Si kL approaching a constant value of tt 2 so that 1 n ykL IfLr 2 L hm R 60 it -kZ. l 4 Er A 17 PROBLEMS Section 9-1 1. We wish to find the properties of waves propagating within a linear dielectric medium that also has an Ohmic conductivity a. a What are Maxwell s equations in this medium b Defining vector and scalar potentials what gauge condition decouples these potentials c A point charge at r 0 varies sinusoidally with time as Q t Re Qe u t . What is the scalar potential d Repeat a - c for waves in a plasma medium with constitutive law dJ _ 2 F - wfeE di 2. An infinite current sheet at z 0 varies as Re K0 a Find the vector and scalar potentials. b What are the electric and magnetic fields 696 Radiation c Repeat a and b if the current is uniformly distributed over a planar slab of thickness 2a iJo a z a 1 0 z a 3. A sphere of radius R has a uniform surface charge distribution oy Re oo where the time varying surface charge is due to a purely radial conduction current. a Find the scalar and vector potentials inside and outside the sphere. Hint TqP r2 R2 2rR cos 0 rQPdrQP rR sin 0 d0. b What are the electric and magnetic fields everywhere Section 4. Find the effective lengths radiation resistances and line charge distributions for each of the following current distributions valid for z dU2 on a point electric dipole with short length dl a I z Io cos az b f z Zoe- il1 c I z Io cosh az 5. What is the time-average power density total time-average power and