Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois, USA Amrita Viswa Vidya Peetham, Coimbatore July 10 – August 11, 2006

1.2 Cartesian Coordinate System

Cartesian Coordinate System

Right-handed system xyz xy… ax, ay, az are uniform unit vectors, that is, the direction of each unit vector is same everywhere in space.

(1)

P1.8 A(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

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

= (2) Differential Length Vector (dl)

= dx ax + f ¢(x) dx ay dl = dx ax + dy ay Unit vector normal to a surface:

D1.5 Find dl along the line and having the projection dz on the z-axis. (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 ± an 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,