Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois, USA Amrita Viswa Vidya Peetham, Coimbatore July 10 – August 11, 2006

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