tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 34

Electromagnetic Field Theory: A Problem Solving Approach Part 34. 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 305 These relations are known as the Cauchy-Riemann equations and u and v are called conjugate functions. c Show that both u and v obey Laplace s equation. d Show that lines of constant u and v are perpendicular to each other in the xy plane. Hint Are Vu and Vv perpendicular vectors Section 9. A half cylindrical shell of length I having inner radius a and outer radius b is composed of two different lossy dielectric materials ei ai for 0 t a and e az for a t it. A step voltage Vo is applied at t 0. Neglect variations with z. a What are the potential and electric field distributions within the shell at times t 0 t co and during the transient interval Hint Assume potentials of the form A t 4 B t and neglect effects of the region outside the half cylindrical shell. b What is the time dependence of the surface charge at 4 a c What is the resistance and capacitance 10. The potential on an infinitely long cylinder is constrained to be V r a Vo sin ruf a Find the potential and electric field everywhere. b The potential is now changed so that it is constant on 306 Electric Field Boundary Value Problems each half of the cylinder Vo 2 V r a. Ị l-Vo 2 0 4 ir ir 4 2ir Write this square wave of potential in a Fourier series. c Use the results of a and b to find the potential and electric field due to this square wave of potential. 11. A cylindrical dielectric shell of inner radius a and outer radius b is placed in free space within a uniform electric field Eoix- What are the potential and electric field distributions everywhere ÍQÍ i cosộ iộ sinộ 12. A permanently polarized cylinder Pa x of radius a is placed within a polarized medium Piix of infinite extent. A uniform electric field o x is applied at infinity. There is no free charge on the cylinder. What are the potential and electric field distributions . Plix l o x Problems 307 13. One type of electrostatic precipitator has a perfectly conducting cylinder of radius a placed within a uniform electric field Toi .