1. University of Utah Advanced Electromagnetics Green’s Function Dr. Sai Ananthanarayanan University of Utah Department of Electrical and Computer Engineering www.ece.utah.edu/~psai 1

2. 2 2D Green’s Function Static Fields

3. 3 2D Green’s Function Static Fields

4. 4 Closed Form Solution Representing the Green’s function by normalized single function Fourier series of sine functions that satisfy the BC: Substituting into the equation below

5. 5 Closed Form Solution And applying

6. 6 Closed Form Solution For Homogeneous case with solutions

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11. 11 Since the cylinder is infinitely long, the solution for potential will not be a function of z. Expanded form of Poisson’s equation reduces to:

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18. 18 Time Harmonic Fields

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20. 20 Considering Homogeneous form:

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24. 24 Whereever singularities are present the frequencies of the excitation sorce matches the natural frequency of the system. This is referred to as resonance.