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
Scalar and Vector Fields 1.4 Scalar and Vector Fields
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.
(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).
Example: Linear velocity vector field of points on a rotating disk
(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)
D1.10 T(x, y, z, t) (a) Constant temperature surfaces are elliptic cylinders,
(b) Constant temperature surfaces are spheres, (c) Constant temperature surfaces are ellipsoids,
Procedure for finding the Equation for the Direction Lines of a Vector Field The field F is tangential to the direction line at all points on a direction line.
Similarly cylindrical spherical
P1.26 (b) (Position vector)
\ Direction lines are straight lines emanating radially from the origin. For the line passing through (1, 2, 3),