Section 2 2 TRƯỜNG ĐIỆN TỪ

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 = 0
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
2

A • dS 0

A • dS

0

2
x

y


2.2-6

(b)

z
2

x 2, an ax

A 2 ax  a y 

d S dy dz ax
A • dS 2 dy dz

2
2
x

2
2

A • dS y 0 z 0 2 dy dz 8

A • dS

8

y


2.2-7

z

(c)

2

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

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

4

3

4
A • dS  3

z

2

x+z=2
y

x

2