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

Gauss’ Law for the Electric Field

Displacement flux emanating from a closed surface S = charge contained in the volume bounded by S = charge enclosed by S.

•

D



3 3

C m , or C m

 D S  



Gauss’ Law for the Magnetic Field

Magnetic flux emanating from a closed

surface S = 0.

B

dS

S

B • dS = 0

S



P2.21 Finding displacement emanating from a surface

enclosing charge

(a) Surface of cube bounded by

x  y  z 

   2 2 2 

0

x y z x y z

0

1 1 1

0 0 0 0

0 0

3

1 1 1

3 3 3 16

x y z

x y z











  

  





  

  

D S 



(b)

Surface of the volume x > 0, y > 0, z > 0, and (x2 + y2 + z2) < 1.

0 0

1

0

0 0

1

48

x

x

x x x x x x x dx

x x x dx x x x















2 2 2

2

2

0

0

0 0

1

1 0 0

0

1 2

2 2 2 4

x

x y

x

x

y

xyz dx dy dz

xy x y dx dy

xy x y xy dx





















    

  

 



D S 



 x y z , ,  0  x y z 

z

y

x  dS3

dS1

dS2

dS4 1

P2.23

B • dS

S



 B • dS + S B • dS 2

2



S 1



 B • dS 3  S B • dS 4

4



S 3



0

1 1

1

1

0

2 0

0 0

2

B x dx dz B









 





 

 



2 0

2

B 