TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 23

Electromagnetic Field Theory: A Problem Solving Approach Part 23. 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. | Lossy Media 195 pf x - 0 Po Figure 3-25 A moving conducting material with velocity i7i tends to take charge injected at x 0 with it. The steady-state charge density decreases exponentially from the source. velocity becomes o n which has exponentially decaying solutions _ -eU pf p e lm 56 57 where lm represents a characteristic spatial decay length. If the system has cross-sectional area A the total charge q in the system is 4 1 pfAdx polmA 58 3-6-6 The Earth and its Atmosphere as a Leaky Spherical Capacitor In fair weather at the earth s surface exists a de electric field with approximate strength of 100 V m directed radially toward the earth s center. The magnitude of the electric field decreases with height above the earth s surface because of the nonuniform electrical conductivity r r of the atmosphere approximated as tr r cr0 a r R 2 siemen m where measurements have shown that o-0 3xlO-14 a .5x IO-20 59 60 M. A. Uman The Earth and Its Atmosphere as a Leaky Spherical Capacitor Am. J. Phys. V. 42 Nov. 1974 pp. 1033-1035. 196 Polarization and Conduction and R 6x IO6 meter is the earth s radius. The conductivity increases with height because of cosmic radiation in the lower atmosphere. Because of solar radiation the atmosphere acts as a perfect conductor above 50 km. In the de steady state charge conservation of Section 3-2-1 with spherical symmetry requires V-J - r7r 0 r a r Er -i 61 r dr r where the constant of integration C is found by specifying the surface electric field 100 V m 68 T At the earth s surface the current density is then Jr R cr R Er R a0Er R -3 x 10-12 amp m2 63 The total current directed radially inwards over the whole earth is then 1 Jr R 4nR2 - 1350 amp 64 The electric field distribution throughout the atmosphere is found from 62 as 7 r 6 r iw iMo- The surface charge density on the earth s surface is af r R e0Er R x IO 10 Coul m2 66 This negative surface charge distribution remember Er r 0 is balanced by positive volume charge .

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