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 1.4 Scalar and Vector Fields 1.4-3 FIELD is a description of how a physical quantity varies from one point to another in the region of the field (and with time) (a) Scalar fields Ex: Depth of a lake, d(x, y) Temperature in a room, T(x, y, z) Depicted graphically by constant magnitude contours or surfaces y d3 d1 d2 x 1.4-4 (b) Vector Fields Ex: Velocity of points on a rotating disk v(x, y) = vx(x, y)ax + vy(x, y)ay Force field in three dimensions F(x, y, z) = Fx(x, y, z)ax + Fy(x, y, z)ay + Fz(x, y, z)az Depicted graphically by constant magnitude contours or surfaces, and direction lines (or stream lines) 1.4-5 Example: Linear velocity vector field of points on a rotating disk 1.4-6 (c) Static Fields Fields not varying with time (d) Dynamic Fields Fields varying with time Ex: Temperature in a room, T(x, y, z; t) 1.4-7 D1.10 T(x, y, z, t) 2 = To x 1 sin t y 1 cos t z 2 (a) T x, y, z , T0 x 1 y 1 1 z T0 x z Constant temperature surfaces are elliptic cylinders, x z const 1.4-8 (b) T x, y, z , 0.5 T0 x 1 1 y 1 z 2 T0 4 x y z Constant temperature surfaces are spheres, x y z const 2 (c) T x, y, z , 1 T0 x 1 y 1 1 z T0 x 16 y z Constant temperature surfaces are ellipsoids, x 16 y z const 1.4-9 Procedure for finding the Equation for the Direction Lines of a Vector Field dl F dl The field F is tangential to the direction line at all points on a direction line F F ax dl F dx Fx ay dy Fy az dz 0 Fz dx dy dz Fx Fy Fz 1.4-10 Similarly dr r d dz Fr F Fz cylindrical dr r d r sin d Fr F F spherical 1.4-11 P1.26 (b)xa x ya y za z (Position vector) dx dy dz x y z ln x ln y ln C1 ln z ln C2 ln x ln C1 y ln C2 z x C1 y C2 z 1.4-12 Direction lines are straight lines emanating radially from the origin For the line passing through (1, 2, 3), C1 (2) C2 (3) 1 C1 , C2 y z x or, 6x 3y 2z