ELECTROMAG THEORY 1
ELECTROMAG THEORY 1 PHY 6346
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This 2 page Class Notes was uploaded by Mrs. Linda Wiegand on Friday September 18, 2015. The Class Notes belongs to PHY 6346 at University of Florida taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/206774/phy-6346-university-of-florida in Physics 2 at University of Florida.
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Date Created: 09/18/15
Chapter 5 Fourier Expansions and Separation of Variables in Rectangular Coordinates Eigenfunctions come naturally in the treatment of vibrations in a con ned space Electro magnetic eigenmodes arise in the same way as their mechanical counterpart7 such as sound waves in organ pipes The basic equation for waves of speed c is 62 1 62 J Z 51 3x2 02 3t in one dimension An eigenmode is sinusoidal in time7 so that the wave equation becomes 62 2 W k 7 07 52 where elk is the angular frequency usually called w The solutions are plane waves epz39kz7 with positive and negative k 51 Convergence If the waves are con ned to a ring of length L7 the eigenfunctions are simply plane waves with k taking the special values eigenvalues kn 27mL7 n integer 53 The expansion f E On expz39kn7 54 with L2 on eXp7 knfdL7 55 7L 2 32