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 d S J • dS + dt V  dv 0 J (t) V S dS Current due to flow of charges emanating from a closed surface S = Time rate of decrease of charge enclosed by S 2.6-4 Summarizing, we have the following: Maxwell’s Equations d C E • dl = – dt B • dS d C H • dl = J • dS + dt D • dS S D • dS = V  dv S B • dS = (1) (2) (3) (4) 2.6-5 Law of Conservation of Charge d S J • dS  dt V  dv 0 (5) (4) is, however, not independent of (1), whereas (3) follows from (2) with the aid of (5) 2.6-6 Example: Finding  H  d l around C C dS I1 S Q(t) I2 C d C H • dl = I2  dt S D • dS (Ampére’s Circuital Law) S D • dS = Q (Gauss’ Law for the electric field and symmetry considerations) 2.6-7 dQ I2 – I1  0 dt (Law of Conservation of charge) dQ  I1 – I2 dt d 1    H  d l I2   Q  C dt   I2   I1  I2    I1  I2 