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. 3.3 Curl and Divergence

3. Maxwell’s Equations in Differential Form
Curl
Divergence

4. Basic definition of curl
is the maximum value of circulation of A per
unit area in the limit that the area shrinks to the point.
Direction of is the direction of the normal
vector to the area in the limit that the area shrinks
to the point, and in the right-hand sense.

5. Curl Meter is a device to probe the field for studying the curl of the
field. It responds to the circulation of the field.

8. ò Ñ Basic definition of divergence Divergence meter A d S Lim g Ñ g A=D v
is the outward flux of A per unit volume in the limit that the volume shrinks to the point.
Divergence meter
is a device to probe the field for studying the divergence of the field. It responds to the closed surface integral of the vector field.

9. Example: At the point (1, 1, 0) (a) Divergence zero (b)
Divergence positive
(c)
Divergence negative

10. Two Useful Theorems: Stokes’ theorem Divergence theorem
A useful identity