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

2.1 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,