Section 2 4 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[.]

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

Ampére’s Circuital Law

Ampére’s Circuital Law

H • dl 

C

dt

S

dS

S C

J, D

 A m m, or A  

H • dl

C



J • dS

S



D • dS

S



= Magnetomotive force (only by analogy with electromotive

force),

= Current due to flow of charges

crossing S,

= Displacement flux, or electric

flux, crossing S,

C m2  m , or C.2

Amp m2  m , or A 2

dt S D •dS = Time rate of increase of

displacement flux crossing S,

or, displacement current

crossing S,

C s, or A

Right-hand screw rule

Any surface S bounded by C, but the same surface

for both terms on the right side

(a) Infinitely long, current carrying wire

No displacement flux

J • dS 

S1

2



H • dl I

C



To  From 

S1

S2

S1

S2 I(t)

J • dS =

S1

 I but S J • dS =

2

D • dS =

S1

 0 but S D • dS 

2

d

dt S2 D • dS must be I

so that H • dlC is unique

(b) Capacitor circuit (neglect fringing of field

in the capacitor)

I C

S1

S2

(c) Finitely long wire

J • dS I and

S1

1



J • dS 0 and

S2

2



J • dS  d

dt

S1

 D • dS must be S

1



 J • dS  d

dt

S2

2



Uniqueness of C H • dl

2

S1

rubber band

potato

H • dl  J • dS1  d

dt

S1



C

1



H • dl – J • dS2 – d

dt

S2



C

2



 J • dS1  d

dt

S1

dt

S2

2



S1



d

dt S1D • dS1  d

dt S2 D • dS2 – S J • dS1

1

2



dt SS1S2 D • dS – SS1S2 J • dS

Displacement current emanating from a closed surface = – (current due to flow of charges

emanating from the same closed surface)

23

23 23

0

3

S

d

dt



D S



Q 2

Q 3

Q 1

3I

S 2

spherical surface of radius 0.1 m and centered at Q1

(c) Displacement current emanating from the spherical

surface of radius 0.1 m and centered at Q3.

3

3

23

23

3 3 3 6

S

S

d

dt

dt

    





D S

D S









1

1

4

S

S

d

dt

dt







D S

D S









E • dl = –

C

 dt d S B • dS

H • dl =

C

dt

S

Magnetic Fields

Hertzian Dipole