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Section2-6 - Slide Presentations for ECE 329 Slide...

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Unformatted text preview: Slide Presentations for ECE 329, Slide Introduction to Electromagnetic Fields, to supplement “Elements of Engineering to Electromagnetics, Sixth Edition” Electromagnetics, 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 ρ dv = 0 J ρ (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 ρ dv (1) (2) (3) (4) ∫S B • dS = 0 2.6-5 Law of Conservation of Charge d ∫S J • dS + dt ∫V ρ 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 ÑH gd l around C. ∫ C dS I1 Q(t) C S I2 d ∫C H • dl = I2 + dt ∫S D • dS (Ampére’s Circuital Law) 1 ∫S D • dS = 2 Q (Gauss’ Law for the electric field and symmetry considerations) 2.6-7 dQ I2 – I1 + =0 dt dQ = I1 – I2 dt (Law of Conservation of charge) d 1 ∴ ÑH gd l = I2 + Q ∫C dt 2 1 = I2 + ( I1 − I2 ) 2 1 = ( I1 + I2 ) 2 ...
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Section2-6 - Slide Presentations for ECE 329 Slide...

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