1. 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

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),