TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 13

Electromagnetic Field Theory: A Problem Solving Approach Part 13. 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. | The Method of Images with Line Charges and Cylinders 95 Figure 2-24 a Two parallel line charges of opposite polarity a distance 2a apart b The equipotential dashed and field solid lines form a set of orthogonal circles. 96 The Electric Field For the field given by 5 the equation for the lines tangent to the electric field is dy Ey 2xy d xz y2 n r- 2 2_2 7 2 2 . 2 m y 0 6 dx Ex y a X a x y where the last equality is written this way so the expression can be directly integrated to 2 x2 y-o cot X2 2 - 7 sin a2 where K. is a constant determined by specifying a single coordinate x0 yo along the field line of interest. The field lines are also circles of radius a sin K with centers at x 0 y a cot K as drawn by the solid lines in Figure 2-246. 2-6-2 The Method of Images a General properties When a conductor is in the vicinity of some charge a surface charge distribution is induced on the conductor in order to terminate the electric field as the field within the equipotential surface is zero. This induced charge distribution itself then contributes to the external electric field subject to the boundary condition that the conductor is an equipotential surface so that the electric field terminates perpendicularly to the surface. In general the solution is difficult to obtain because the surface charge distribution cannot be known until the field is known so that we can use the boundary condition of Section . However the field solution cannot be found until the surface charge distribution is known. However for a few simple geometries the field solution can be found by replacing the conducting surface by equivalent charges within the conducting body called images that guarantee that all boundary conditions are satisfied. Once the image charges are known the problem is solved as if the conductor were not present but with a charge distribution composed of the original charges plus the image charges. b Line Charge Near a Conducting Plane The method of images can adapt a .

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