Section 2 5 TRƯỜNG ĐIỆN TỪ

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 2.5 Gauss’ Laws 2.5-3 Gauss’ Law for the Electric Field  C  S D  dS V  dv  m3 m , or C  D • V S dS Displacement flux emanating from a closed surface S = charge contained in the volume bounded by S = charge enclosed by S 2.5-4 Gauss’ Law for the Magnetic Field S B • dS = B S Magnetic flux emanating from a closed surface S = 0 dS 2.5-5 P2.21 Finding displacement emanating from a surface enclosing charge  (a)   x, y, z  0  x  y  z 2  Surface of cube bounded by x 1, y 1, and z 1  D  d S   dv    S V 1 x  y  z  1 8 0  0 3  x2  y2  z  dx dy dz   3  x 1 x 0 y 0 z 0 1 1  8 0      3 3  16 0  y2  z  dx dy dz 2.5-6 (b)   x, y, z  0  x y z  Surface of the volume x > 0, y > 0, z > 0, and (x2 + y2 + z2) <  D  d S   dv S V  1 x2 1 x2  y2   0 xyz dx dy dz 1 x2 xy 1  x2  y2  dx dy x 0 y 0 z 0     0   xy x y xy  x0     dx y 0    3 5  x  x  x  x  x  x  x dx   x0    0  0  x2 x4 x6   x 5 x0   x  x  dx     12   0 48 x 0 y 0 1 x2 1 2.5-7 P2.23 z dS4 dS1 dS2 x y  dS3 S B • dS   B • dS +  B • dS2 S1 S2  S B • dS3  S B • dS 4 0 2.5-8   B  d S1 S1   B  d S2  S2     z 0 x 0 B0  B  dS   B  dS  ya  xa    dx dz a  S3 x y y 0  0     z 0 x 0 B0  B0 x dx dz B0  Absolute value = Wb S4 y