tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 59

Electromagnetic Field Theory: A Problem Solving Approach Part 59. 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 555 b Obtain a single equation in Ex. c Jf the fields vary sinusoidally with time Ex Re x z what are the spatial dependences of the fields d Specialize c to the i low loss limit cr we 1 and ii large loss limit a ae 1 . e Repeat a - c if the medium is a plasma with constitutive law dj 2 P a tsE dt f A current sheet Ko cos a tix is placed at z 0. Find the electric and magnetic fields if the sheet is placed within an Ohmic conductor or within a plasma. 9. A uniformly distributed volume current of thickness 2d Jo cos a tix is a source of plane waves. 6o MO ----2d---- a From Maxwell s equations obtain a single differential equation relating Ex to Jx. b Find the electric and magnetic fields within and outside the current distribution. c How much time-average power per unit area is delivered by the current d How does this generated power compare to the electromagnetic time-average power per unit area leaving the volume current at z d 10. A TEM wave Ex H propagates in a medium whose permittivity and permeability are functions of z e z and jiz z . a Write down Maxwell s equations and obtain single partial differential equations in Ex and Hr b Consider the idealized case where e z ee z and p. z z . A current sheet K oe w ix is at z 0. What are 556 Electrodynamics Fields and Waves the resulting electric and magnetic fields on each side of the sheet c For what values of a are the solutions spatially evanescent or oscillatory 11. We wish to compare various measurements between two observers the second moving at a constant velocity vit with respect to the first. a The first observer measures simultaneous events at two positions zi and z2 so that fi i2. What is the time interval between the two events t i tí as measured by the second observer b The first observer measures a time interval Aí ti 12 between two events at the same position z. What is the time interval as measured by the second observer c The first observer measures the length of a stick as L z2 Zi. What