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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

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By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

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


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • 1.6

  • The Magnetic Field


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • The Magnetic Field

  • acts to exert force on charge when it is in motion.

  • B = Magnetic flux density vector

  • Alternatively, since charge in motion constitutes current, magnetic field exerts forces on current elements.


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Units of B:

  • Sources:Currents;

  • Time-varying electric field


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Ampère’s Law of Force


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Magnetic field due to a current element

  • (Biot-Savart Law)

a

B circular to the axis of the current element


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Ex.


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Current Distributions

  • Filamentary Current

  • I (A)

  • (b)Surface Current

  • Surface current density, JS (A/m)


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • (c)Volume Current

  • Density, J (A/m2)


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

P(r, f, z)

a2

a

a1

  • P1.44


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • For infinitely long wire,


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Magnetic Field Due to an Infinite Plane Sheet of Uniform Surface Current Density

  • This can be found by dividing the sheet into infinitely long strips parallel to the current density and using superposition, as in the case of finding the electric field due to an infinite plane sheet of uniform surface charge density. Instead of going through this procedure, let us use analogy. To do this, we first note the following:


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

  • Point ChargeCurrent Element


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

rL0

  • (b)Line ChargeLine Current


By nannapaneni narayana rao edward c jordan professor of electrical and computer engineering

rS0

  • Then,

  • (c)Sheet ChargeSheet Current


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