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

1.2-2 Cartesian Coordinate System

1.2-3 Right-handed system xyz xy… a x, a y, a z are uniform unit vectors, that is, the direction of each unit vector is same everywhere in space.

1.2-4 (1)

1.2-5

1.2-6 P1.8A(12, 0, 0), B(0, 15, 0), C(0, 0, –20). (a)Distance from B to C = (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

1.2-7 (c)Perpendicular distance from A to the line through B and C =

1.2-8 = (2)Differential Length Vector (dl)

1.2-9 dl=dx a x + dy a y =dx a x + f (x) dx a y Unit vector normal to a surface :

D1.5Find dl along the line and having the projection dz on the z-axis. (a) (b)

(c)Line passing through (0, 2, 0) and (0, 0, 1).

(3)Differential Surface Vector (dS) Orientation of the surface is defined uniquely by the normal ± a n to the surface. For example, in Cartesian coordinates, dS in any plane parallel to the xy plane is

(4)Differential Volume (dv) In Cartesian coordinates,