Post on 13-Dec-2015
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
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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