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

3.3 Curl and Divergence

Maxwell’s Equations in Differential Form Curl Divergence

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.

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

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.

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

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