No Slide Title Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jor[.]
Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India 1.2 Cartesian Coordinate System 1.2-3 Cartesian Coordinate System z az O ay ax y x az ax ay z x y 1.2-4 Right-handed system a x a y a z a y a z a x xyz xy… a z a x a y ax, ay, az are uniform unit vectors, that is, the direction of each unit vector is same everywhere in space 1.2-5 (1) Vector from P1 x1 , y1 , z1 to P2 x2 , y2 , z2 z r1 R12 r2 P1 R12 r2 r1 P2 r2 r1 O x2ax y2a y z2az x1ax y1a y z1az R12 x x2 x1 ax y2 y1 a y z2 z1 az y 1.2-6 z R12 P1 (x – x1)ax x1 x x2 r1 O z1 r2 (y2 – y1)ay y1 P2 (z2 – z1)az z2 y2 y 1.2-7 P1.8 A(12, 0, 0), B(0, 15, 0), C(0, 0, –20) (a) Distance from B to C =(0 – 0)a x (0 – 15)a y (–20 – 0)a z = 15 20 25 (b) Component of vector from A to C along vector from B to C = Vector from A to C • Unit vector along vector from B to C 1.2-8 12ax 20az 15a y 20az 15a y 20az 400 16 25 (c)Perpendicular distance from A to the line through B and C (Vector from A to C) (Vector from B to C) = BC 12ax 20az 15a y 25 20az 1.2-9 = (2) 180a z – 240a y – 300a x 25 = 12 Differential Length Vector (dl) az dl P x, y , z Q x dx, y dy, z dz dx dz ax dy ay dl dx a x dy a y dz a z 1.2-10 dl dx y = f(x) z = constant plane dy = f (x) dx dz = dl = dx ax + dy ay = dx ax + f (x) dx ay Unit vector normal to a surface: dl1 dl an dl1 dl an dl2 dl1 Curve Curve 1.2-11 D1.5 Find dl along the line and having the projection dz on the z-axis (a) x 3, y –4 dx 0, dy 0 dl dz a z x y 0, y z 1 (b) dx dy 0, dy dz 0 dy – dz, dx – dy dz d l dz ax dz a y dz az ax a y az dz 1.2-12 (c)Line passing through (0, 2, 0) and (0, 0, 1) dy dz x 0, – –0 dx 0, dy – dz d l dz a y dz az 2a y az dz 1.2-13 (3) Differential Surface Vector (dS) dS dl1 dl2 sin d l1 × d l2 an dl2 dS dl1 Orientation of the surface is defined uniquely by the normal ± an to the surface dS dS a n dl1 dl a n dl1 dl For example, in Cartesian coordinates, dS in any plane parallel to the xy plane is az dx dy a z dx a x dy a y dy dx dS x y 1.2-14 (4) Differential Volume (dv) dv dl1 • dl dl3 dl2 dl3 dv dl1 In Cartesian coordinates, dv dx a x • dy a y dz a z dx dy dz dz z dy dx y x