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# Section2-2 - Slide Presentations for ECE 329 Introduction...

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Unformatted text preview: Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of to Engineering Electromagnetics, Sixth Edition” Edition” by by 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 Nannapaneni Narayana Rao 2.2 The Surface Integral 2.2-3 The Surface Integral Flux of a vector crossing a surface: B an ∆S B ∆S B an α Flux = (B)(∆ S) an Flux = 0 Flux = ( B cos α ) ∆S = B ∆S cos α = B • ∆S a n = B • ∆S ∆S 2.2-4 Normal anj αj ∆ Sj S Bj Flux = = j =1 n j =1 ∑ ∆ψ j ∑B j • ∆S j n In the limit n → ∞ , Flux, ψ = ∫S B • dS = Surface integral of B over S. 2.2-5 = ∫S B • dS Surface integral of B D2.4 over the closed surface S. z 2 y A = x ( ax + a y ) x = 0, a n = ± a x (a) A = 0, A • d S = 0 ∫ A • dS = 0 ∫ A • dS =0 x 2 2.2-6 (b) A = 2 ( ax + a y ) x = 2, an = ± ax z 2 y d S = ± dy dz ax A • dS = ± 2 dy dz 2 x 2 2 2 ∫ A • dS = ± ∫y =0 ∫z =0 2 dy dz = ± 8 ∫ A • dS = 8 2.2-7 z (c) A = x ( ax + a y ) y = 0, an = ± a y 2 d S = ± dz dx a y A gd S = ± x dx dz y 2 x 2 2 ∫ A • dS = ± ∫x =0 ∫z =0 x dx dz = ± 4 ∫ A • dS =4 2.2-8 (d) From (c), A • dS = ± x dx dz 2– x 2 ∫ A • dS = ± ∫x =0 ∫z =0 x dx dz 2 = ± ∫0 x (2 – x ) dx z 2 x+z=2 y x 2 4 =± 3 4 ∫ A • dS = 3 ...
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Section2-2 - Slide Presentations for ECE 329 Introduction...

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