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

3.4 Uniform Plane Waves in Time Domain in Free Space

3.4-2 Infinite Plane Current Sheet Source: Example:

3.4-3 For a current distribution having only an x-component of current density that varies only with z,

3.4-4 The only relevant equations are: Thus,

3.4-5 In the free space on either side of the sheet, J x = 0 Combining, we get Wave Equation

3.4-6 Solution to the Wave Equation:

3.4-7 represents a traveling wave propagating in the +z-direction. represents a traveling wave propagating in the –z-direction. Where velocity of light

3.4-8 Examples of Traveling Waves:

3.4-9

3.4-10

Thus, the general solution is For the particular case of the infinite plane current sheet in the z = 0 plane, there can only be a (  ) wave for z > 0 and a (  ) wave for z < 0. Therefore,

Applying Faraday’s law in integral form to the rectangular closed path abcda is the limit that the sides bc and da 

Therefore, Now, applying Ampere’s circuital law in integral form to the rectangular closed path efgha is the limit that the sides fg and he  0,

Uniform plane waves propagating away from the sheet to either side with velocity v p = c. Thus, the solution is

x y z z = 0

x y z z = 0 z > 0z < 0  z z

3.4-17

3.4-18