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No Slide Title Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jor[.]
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 2.1-3 The Line Integral Work done in carrying a charge from A to B in an electric field: B E1 A 1 l1 n E2 2 l2 WAB dWj j1 2.1-4 dW j qE j cos j l j qE j l j cos j qE j l j n WAB q E j • l j j1 n WAB VAB E j • l j (Voltage between q A and B) j1 2.1-5 In the limit n , B VAB E • dl A = Line integral of E from A to B C E • dl = Line integral of E around the closed path C 2.1-6 A If R C C L B C E • dl = , B then E • dl A is independent of the path from A to B (conservative field) ARBLA E • dl ARB E • dl BLA E • dl ARB E • dl – ALB E • dl 0 ARB E • dl ALB E • dl 2.1-7 Ex For F yza x zxa y xya z , find (1,2,3) F • dl 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) z (0, 0, 0) (1, 0, 0) x (1, 2, 3) y (1, 2, 0) 2.1-8 From (0, 0, 0) to (1, 0, 0), y z 0 ; dy dz 0 F 0 , (1,0,0) (0,0,0) F • dl 0 From (1, 0, 0) to (1, 2, 0), x 1, z 0 ; dx dz 0 F ya z dl dx a x dy a y dz a z dy a y F • dl 0, (1,2,0) (1,0,0) F • dl 0 2.1-9 From (1, 2, 0) to (1, 2, 3), x 1, y 2 ; dx dy 0 F 2za x za y 2a z , dl dz a z F • dl 2 dz , (1,2,3) (1,2,3) (1,2,0) dz 6 (0,0,0) F • dl 0 6 2.1-10 In fact, F d l yza x zxa y xyaz dx ax dy a y dz az yz dx zx dy xy dz d xyz 1,2,3 0,0,0 1,2,3 F d l 0,0,0 1,2,3 0,0,0 d xyz xyz 12 3 0 0 6, independent of the path