Electromagnetic Field Theory: A Problem Solving Approach Part 42. 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 385 Hoiz c Repeat a and b if we have an infinite array of such dipoles. Hint d If we assume that there is one such dipole within each volume of a3 what is the permeability of the medium 23. An orbiting electron with magnetic moment mziz is in a uniform magnetic field Boiz when at t 0 it is slightly displaced so that its angular momentum L 2mje m now also has x and y components. a Show that the torque equation can be put in terms of the magnetic moment dm --- ym X B dt where y is called the gyromagnetic ratio. What is -y b Write out the three components of a and solve for the magnetic moment if at t 0 the moment is initially m t 0 mxOix myo wz liz c Show that the magnetic moment precesses about the applied magnetic field. What is the precessional frequency 24. What are the B H and M fields and the resulting magnetization currents for the following cases a A uniformly distributed volume current Joiz through a cylinder of radius a and permeability fj. surrounded by free space. b A current sheet Aoiz centered within a permeable slab of thickness d surrounded by free space. 386 Ttừ Magnetic Field Mo a b Section 25. A magnetic field with magnitude Hi is incident upon the flat interface separating two different linearly permeable materials at an angle from the normal. There is no surface current on the interface. What is the magnitude and angle of the magnetic field in region 2 26. A cylinder of radius a and length L is permanently magnetized as M Ặt. a What are the B and H fields everywhere along its axis b What are thè fields far from the magnet r a r L c Use the results of a to find the B and H fields everywhere due to a permanently magnetized slab Moiz of infinite xy extent and thickness L. d Repeat a and b if the- cylinder has magnetization Af0 l r a iz. Hint dr a2 r2 1 2 In r Va2 rẳ Problems 387 z Section 27. A z-directed line current 1 is a distance d above the interface separating two different magnetic materials with permeabilities ti and 2. a .
