Electromagnetic Field Theory: A Problem Solving Approach Part 4

Electromagnetic Field Theory: A Problem Solving Approach Part 4. 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. | Coordinate Systems 5 M Figure 1-2 Circular cylindrical coordinate system a Intersection of planes of constant z and j with a cylinder of constant radius r defines the coordinates r t z . b The direction of the unit vectors ir and i vary with the angle j . c Differential volume and surface area elements. angle 4 from the x axis as defined for the cylindrical coordinate system and a cone at angle 0 from the z axis. The unit vectors ir i and i j are perpendicular to each of these surfaces and change direction from point to point. The triplet r 8 must form a right-handed set of coordinates. The differential-size spherical volume element formed by considering incremental displacements dr r dff r sin dd 6 Review of Vector Analysis Figure 1-3 Spherical coordinate system a Intersection of plane of constant angle with cone of constant angle 9 and sphere of constant radius r defines the coordinates r 6 j . b Differential volume and surface area elements. Vector Algebra 7 Table 1-2 Geometric relations between coordinates and unit vectors for Cartesian cylindrical and spherical coordinate systems CARTESIAN CYLINDRICAL SPHERICAL X r cos 4 r sin 0 cos 4 y r sin f r sin 0 sin 6 z z r cos 0 lx cos 4 ir sin sin 0 cos 6ir cos 0 cos f i9 sin i sin f ir cos 4 U sin 0 sin f ir cos 0sin f i cos f i it cos 0ir - sin 0ie CYLINDRICAL CARTESIAN SPHERICAL r Vx2 y2 r sin 0 tan-1 X 4 z z r cos 0 îr cos 6i sin 4 iy sin 0ir cos 0ig u sin c i cos 6 i u h it cos 0ir - sin 0ie SPHERICAL CARTESIAN CYLINDRICAL r Vx2 y2 z2 Vr2 z2 0 -1 z -i z cos 2 y2 z2 Jr2 z2 6 cot - y t ir sin 0 cos 4 ix sin 0 sin 6i cos 0iz sin 0ir cos 0iz i cos 0 cos 4 ix cos 0 sin 6i sin 0iz cos 0ir sin 0iz u sin 6ix cos 6i U Note that throughout this text a lower case roman r is used for the cylindrical radial coordinate while an italicized r is used for die spherical radial coordinate. from the coordinate r 0 now depends on the angle 0 and the radial position r as shown in Figure 1-36 and summarized in Table 1-1. Table 1-2 .