TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 15

Electromagnetic Field Theory: A Problem Solving Approach Part 15. 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 115 when a the charges have the same polarity q q q q4 q b the charges alternate in polarity i 2 4 -fl c the charges are q q q q 4 q. Section 12. Find the total charge in each of the following distributions where a is a constant parameter a An infinitely long line charge with density A z Ao _ z a b A spherically symmetric volume charge distributed over all space x f O P r r1 _i_ I I4 1 r a Hint Let u 1 ria. c An infinite sheet of surface charge with density - x a T q cr x y --------5- y 1 13. A point charge q with mass M in a gravity field g is released from rest a distance Xo above a sheet of surface charge with uniform density r0. t q a What is the position of the charge as a function of time b For what value of cr0 will the charge remain stationary c If tr0 is less than the value of b at what time and with what velocity will the charge reach the sheet z I 14. A point charge q at z 0 is a distance D away from an X infinitely long line charge with uniform density Ao- a What is the force on the point charge 7 b What is the force on the line charge c Repeat a and b if the line charge has a distribution IM Zl A 2 ----D---- 116 The Electric Field 15. A small sphere of mass M in a gravity field g carrying a charge Q is connected by a massless string to a sheet of surface charge of the same polarity with density a0. What is the angle 0 between the sheet and charge 16. A line charge A along the z axis extends over the interval - z . a Find the electric field in the z 0 plane. b Using the results of a find the electric field in the z 0 plane due to an infinite strip oo y oo of height 2 with Problems 117 surface charge density r0. Check your results with the text for L- oo. Hint Let u x2 y2 r du 1 . -i 2 x2 -2L2x2 J uVu x2 Vls u Lx u L2 x2 17. An infinitely long hollow semi-cylinder of radius R carries a uniform surface charge distribution oq. a What is the electric field along the axis of the cylinder b Use the results of a to find the electric field along .

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