By David K. Cheng
Basic of Engineering Electromagnetics not just provides the basics of electromagnetism in a concise and logical demeanour, but additionally features a number of attention-grabbing and significant purposes. whereas tailored from his well known and extra large paintings, box and Wave Electromagnetics, this article includes a variety of leading edge pedagogical positive aspects. every one bankruptcy starts with an outline which serves to provide qualitative information to the subject material and encourage the coed. evaluation questions and labored examples all through each one bankruptcy toughen the student's figuring out of the cloth. comments containers following the evaluation questions and margin notes in the course of the booklet function extra pedagogical aids.
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Extra resources for Fundamentals of Engineering Electromagnetics
5 + a =S. U. ing Eqs. (2-40a, b, and c). we obtain the Carte ian coordinates of the point Pas (4cos60 ', 4sin60 ', 5), or (2, 2vfi, 5). 6 Expres the position vector OQ from the origin O to the point Q(3, 4, 5) in cylindrical coordinates. 1) and P 1 (3. 180. - l). Dercrmine the distance berween these two points. • ANS. , 41. :-ax is and having a half-angle 0 = 0 1 ; and a half-plane with the z-axis as an edge and making an angle¢= > 1 with the xz-plane. We have (111, ll2. U3) = (R. 0, (/>). The three intersecting surfaces are shown in Fig.
Will. of course, depend on the choice of the coord inate system. We shall now derive the expression for div A in Carte ian coordinates. Consider a differential volume of sides f1x , f1 y, and f1 z centered about a point P(x 0 , y 0 , 2 0 ) in the field of a vec tor A, as shown in Fig. 2-18. A =. -:: 0 ). Since the differential volume has six face , the surface integral in the numerator of Eq . (2-58) can be decomposed into ix parts: 1 1 lJs_A . r, + (op + l~ouom] A. ds. (2-59) ~ace J~ace J} J J}ace J!
PJ. r=R'>ine . =U co~ (} \' x 2-4 ORTHOGONAL COORDI ATE SYSTEMS 37 EXAMPLE 2-7 Express the unit vector a= in spherical coordinates. SOLUTION First of all, we must not be tempted by Eq. (2-45c) to write a= as aR R cos f) or aR cos(:) because both the direction (a= # aR) and the magnitude (I # R cos or cos 0 for all 0) would be incorrect. Since the base vectors for spherical coordinate arc aR , a6 and a4>, let us proceed by finding the components of a= in thee directions. From Figs. 2-13 and 2-14 we have e a=·aR = COSfJ.