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

2.1 The Line Integral

Work done in carrying a charge from A to B in an electric field: The Line Integral Work done in carrying a charge from A to B in an electric field: a1 a2

(Voltage between A and B)

In the limit , = Line integral of E from A to B. = Line integral of E around the closed path C.

is independent of the path from A to B (conservative field)

along the straight line paths (0, 0, 0) Ex. For find (1,2,3) along the straight line paths (0, 0, 0) from (0, 0, 0) to (1, 0, 0), from (1, 0, 0) to (1, 2, 0) and then from (1, 2, 0) to (1, 2, 3).

From (0, 0, 0) to (1, 0, 0), From (1, 0, 0) to (1, 2, 0),

From (1, 2, 0) to (1, 2, 3),

In fact,