Section 2 6 TRƯỜNG ĐIỆN TỪ

2 6 The Law of Conservation of Charge Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Na[.]

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

2.6 The Law of Conservation of Charge

2.6-3 Law of Conservation of Charge

Current due to flow of charges emanating from a closed surface S =

Time rate of decrease of charge

enclosed by S.

J• dS + d

dt V  dv 0 S



J

S

(t)

Summarizing, we have the following:

Maxwell’s Equations

E • dl = – d

dt

C

H • dl = J • dS + d

dt

C

D • dS = V  dv

S



B • dS = 0

S



(1)

(2) (3) (4)

Law of Conservation of Charge

(4) is, however, not independent of (1), whereas (3) follows from (2) with the aid of (5)

J • dS 

S

 dt d V  dv 0 (5)

I 1

dS

I2 Q(t) C

S

H • dl = I2  d

dt S D •dS

C



(Ampére’s Circuital Law)

D • dS = 1

2

S

and symmetry considerations)

Finding  C H  dl around C

Example:

2

C

d

dt

  H  l    

I2 – I1  dQ

dt 0 (Law of Conservation of charge)

dQ

dt  I1 – I2

1 2 1

2

I I

  