Section 2 4 TRƯỜNG ĐIỆN TỪ

No Slide Title Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jor[.]

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 2.4 Ampére’s Circuital Law 2.4-3 Ampére’s Circuital Law d C H • dl  S J • dS  dt S D • dS J, D S C dS 2.4-4 C H • dl = Magnetomotive force (only by analogy with electromotive force), A m  m, or A S J • dS = Current due to flow of charges crossing S, Amp m2  m2 , or A  S D • dS  = Displacement flux, or electric flux, crossing S, 2 C m  m , or C 2.4-5 d D • dS = Time rate of increase of  S dt displacement flux crossing S, or, displacement current crossing S, C s, or A Right-hand screw rule Any surface S bounded by C, but the same surface for both terms on the right side 2.4-6 Three cases fo clarify Ampére’s circuital law (a) Infinitely long, current carrying wire No displacement flux S1 J • dS  S2 J • dS  I C H • dl I S1 From  C I S2 To  2.4-7 (b) Capacitor circuit (neglect fringing of field in the capacitor) S2 C I(t) S1 S1 J • dS = I but S2 J • dS = S1 D • dS = but S2 D • dS  d D • dS must be I  S dt so that C H • dl is unique 2.4-8 (c) Finitely long wire S1 J • dS I and S1 D • dS 0 S2 J • dS 0 and S2 D • dS 0 d S1 J • dS  dt S1 D • dS must be d   J • dS  D • dS  S2 S dt S1 Q1 I C Q2 S2 2.4-9 Uniqueness of C H • dl dS1 S1 dS2 C S2 potato rubber band d D • dS1  C S1 S dt d H • dl  – J • dS – C S2  D • dS dt S2 d d  S J • dS1  S D • dS1 – S J • dS – S D • dS 2 dt dt d d D • dS    D • dS – S1 J • dS1 – S2 J • dS2 dt S1 dt S2  H • dl   J • dS1  2.4-10 d D • dS – J • dS   SS1 S2 dt SS1 S2 Displacement current emanating from a closed surface = – (current due to flow of charges emanating from the same closed surface) 2.4-11 D2.9 (a) Current flowing from Q2 to Q3 d  I  I23  D  d S 0 dt S2  I  I23  I 0 Q2 I23 3I A I23 I Q1 3I S1 S2 Q3 S3 2.4-12 (b) Displacement current emanating from the spherical surface of radius 0.1 m and centered at Q1 d I  3I  D  d S 0 dt S1 d D  d S  I A   dt S1 (c) Displacement current emanating from the spherical surface of radius 0.1 m and centered at Q3 d  3I  I23  D  d S 0 dt S3 d D  d S 3I  I23 3I  3I 6 I A   dt S3 2.4-13 Interdependence of Time-Varying Electric and Magnetic Fields d C E • dl = – dt S B • dS d C H • dl = S J • dS + dt S D • dS 2.4-14 Hertzian Dipole I(t) I(t) H(t) E(t)