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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
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2 2D Green’s Function Static Fields
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3 2D Green’s Function Static Fields
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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
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5 Closed Form Solution And applying
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6 Closed Form Solution For Homogeneous case with solutions
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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 Time Harmonic Fields
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20 Considering Homogeneous form:
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24 Whereever singularities are present the frequencies of the excitation sorce matches the natural frequency of the system. This is referred to as resonance.
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