1. 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

2. Scalar and Vector Fields
1.4
Scalar and Vector Fields

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.

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).

5. Example: Linear velocity vector field of points on a
rotating disk

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)

7. D1.10 T(x, y, z, t)
(a)
Constant temperature surfaces are elliptic cylinders,

8. (b)
Constant temperature surfaces are spheres,
(c)
Constant temperature surfaces are ellipsoids,

9. 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.

10. Similarly
cylindrical
spherical

11. P1.26 (b)
(Position vector)

12. \ Direction lines are straight lines emanating radially from the origin. For the line passing through (1, 2, 3),