tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 28

Electromagnetic Field Theory: A Problem Solving Approach Part 28. 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 245 36. Charge maintained at constant density p0 at x 0 is carried away by a conducting fluid travelling at constant velocity Uix and is collected at x I. e Ơ t II TTTTTTTTTT I j Cross-sectional I area A I I -I------------------------1- x 0 . a What are the field and charge distributions within the fluid if the electrodes are at potential difference Vo b What is the force on the fluid c Repeat a and b if the voltage source is replaced by a load resistor RL. 37. A de voltage has been applied a long time to an open circuited resistive-capacitive structure so that the voltage and current have their steady-state distributions as given by 44 . Find the resulting discharging transients for voltage and current if at t 0 the terminals at z 0 are suddenly a open circuited. Hint t m7FZ mrr sinhaỉ sinh a z-l sin I I dz --T r st . v2 Io I I a mir l b Short circuited. Hint f 1 m cosh a z -1 sin I----- ------1 Jo 2i 2n l ir cosh al 38. At t 0 a distributed resistive line as described in Section 3-6-4 has a step de voltage Vo applied at z 0. The other end at z I is short circuited. a What are the steady-state voltage and current distributions b What is the time dependence of the voltage and current during the transient interval Hint mirz m-rr sinh al j J dz ------------------- a2 nnr 2j 246 Polarization and Conduction 39. A distributed resistive line is excited at z 0 with a sinusoidal voltage source v t Vo cos tot that has been on for a long time. The other end at z I is either open or short circuited. a Using complex phasor notation of the form v z t Re v z find the sinusoidal steady-state voltage and current distributions for each termination. b What are the complex natural frequencies of the system c How much time average power is delivered by the source 40. A lossy dielectric with permittivity e and Ohmic conductivity a is placed between coaxial cylindrical electrodes with large Ohmic conductivity ac and length I. What is the series resistance per unit length 2R of