Electromagnetic Field Theory: A Problem Solving Approach Part 10. 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. | Charge Distributions 65 Figure 2-11 An infinitely long uniform distribution of line charge only has a radially directed electric field because the z components of the electric field are canceled out by symmetrically located incremental charge elements as also shown in Figure 2-8a. 2-3-4 Field Due to Infinite Sheets of Surface Charge a Single Sheet A surface charge sheet of infinite extent in the y 0 plane has a uniform surface charge density oq as in Figure 2-12a. We break the sheet into many incremental line charges of thickness dx with dX. a0 dx. We could equivalently break the surface into incremental horizontal line charges of thickness dz. Each incremental line charge alone has a radial field component as given by 5 that in Cartesian coordinates results in x and y components. Consider the line charge dA i a distance x to the left of P and the symmetrically placed line charge dA2 the same distance x to the right of P. The x components of the resultant fields cancel while the y 66 The Electric Field Op z ơ Op 2ep Op 2ep I 1 II 2 III v ơo o b Figure 2-12 a The electric field from a uniformly surface charged sheet of infinite extent is found by summing the contributions from each incremental line charge element. Symmetrically placed line charge elements have x field components that cancel but y field components that add. 6 Two parallel but oppositely charged sheets of surface charge have fields that add in the region between the sheets but cancel outside c The electric field from a volume charge distribution is obtained by summing the contributions from each incremental surface charge element. Charge Distributions 67 components add _ a-pdx _ aoydx 2mo x2 j2 1 2C 2OTo x2 j2 6 The total field is then obtained by integration over all line charge elements i oo J dx 2 . 2 _ -co x y 1 I 00 TOy 1 X --------tan - 2ir Oy y 1 oo Oo 2e0 -a0 2e0 7 where we realized that the inverse tangent term takes the sign of the ratio x y so that the field reverses direction on each side
