Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement

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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
• University of Illinois at Urbana-Champaign,
  Urbana, Illinois, USA
• Distinguished Amrita Professor of Engineering
• Amrita Vishwa Vidyapeetham, Coimbatore, Tamil
  Nadu, India

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• 3.1
• Faradays Law and
• Ampères Circuital Law

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• Maxwells Equations in Differential Form
• Why differential form?
• Because for integral forms to be useful, an a
  priori knowledge of the behavior of the field to
  be computed is necessary.
• The problem is similar to the following
• There is no unique solution to this.

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• However, if, e.g., y(x) Cx, then we can find
  y(x), since then
• On the other hand, suppose we have the following
  problem
• Then y(x) 2x C.
• Thus the solution is unique to within a constant.

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• FARADAYS LAW
• First consider the special case
• and apply the integral form to the rectangular
  path shown, in the limit that the rectangle
  shrinks to a point.

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• General Case

Lateral space derivatives of the components of E
Time derivatives of the components of B
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• Combining into a single differential equation,

Differential form of Faradays Law
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• AMPÈRES CIRCUITAL LAW
• Consider the general case first. Then noting
  that
• we obtain from analogy,

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• Thus
• Special case

Differential form of Ampères circuital law
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Ex. For in free space find the value(s) of k
such that E satisfies both of Maxwells curl
equations. Noting that
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• Thus,

Then, noting that we
have from
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Comparing with the original given E, we have
Sinusoidal traveling waves in free space,
propagating in the z directions with
velocity,