Section 2 2 TRƯỜNG ĐIỆN TỪ

Slide 1 Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jordan Pro[.]

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 2.2 The Surface Integral 2.2-3 The Surface Integral Flux of a vector crossing a surface: B an S Flux = (B)(S) B S B an  S an Flux = Flux (B cos  ) S B S cos  B • S a n B • S 2.2-4 Normal anj j Bj Flux    j j1 n Sj S   B j • S j In the limit n   , Flux,  = n j1 S B • dS = Surface integral of B over S 2.2-5 S B • dS= Surface integral of B over the closed surface S A  x ax  a y  (a) x 0, a n a x A 0, A • dS 0 D2.4 z A • dS 0 A • dS 0 x y 2.2-6 (b) z x 2, an ax A 2 ax  a y  d S dy dz ax A • dS 2 dy dz 2 x 2 A • dS y 0 z 0 dy dz 8 A • dS 8 y 2.2-7 z (c) y 0, an a y A  x ax  a y  d S dz dx a y A  d S  x dx dz y x 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 A • dS x0 z 0 x dx dz 0 x(2 – x) dx  A • dS  z x+z=2 y x