Edward C. Jordan Memorial Offering of the First Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Course under the Indo-US Inter-University

Collaborative Initiative in Higher Education and Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Research: Electromagnetics for Electrical and

Computer EngineeringComputer Engineering

byby

Nannapaneni Narayana RaoNannapaneni Narayana RaoEdward C. Jordan Professor of Electrical and Computer EngineeringEdward C. Jordan Professor of Electrical and Computer Engineering

University of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-ChampaignUrbana, Illinois, USAUrbana, Illinois, USA

Amrita Viswa Vidya Peetham, CoimbatoreAmrita Viswa Vidya Peetham, CoimbatoreJuly 10 – August 11, 2006July 10 – August 11, 2006

2.6

The Law ofConservation 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 chargeenclosed by S.

J • dS +d

dt dv 0

VS

VdS

J

S

(t)

2.6-4

Summarizing, we have the following:

Maxwell’s Equations

E • dl = –d

dtC B • dS

H • dl = J • dS +d

dtC D • dSD • dS = dv

VSB • dS = 0S

(1)

(2)

(3)

(4)

2.6-5

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

d

dt dv 0

V (5)

2.6-6

I1

dS

I2

Q(t) C

S

H • dl = I2 d

dtD •dSSC(Ampére’s Circuital Law)

D • dS =1

2S Q (Gauss’ Law for the electric field and symmetry considerations)

Finding around .C

d CH lExample:

2.6-7

2

1

2C

dd I Q

dt H l

I2 – I1 dQ

dt0

(Law of Conservation of charge)

dQ

dt I1 – I2

2 1 2

1 2

1

21

2

I I I

I I