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9 - Electromagnetics Workshop – Week 9 Solutions...

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Unformatted text preview: Electromagnetics Workshop – Week 9 Solutions Electrostatic Potential and Divergence Theorem Problem 1: Find the electrostatic potential at (0, 0, 5) [m] in air produced by: a) 8 [nC] distributed as a uniform ring of charge at z = , 1 ρ = [m]; b) four point charges, 2 [nC] each, at ( ± 1, 0, 0) [m] and (0, ± 1, 0) [m]. Assume ( 29 Φ ∞ = . Solution: Since the total charge is the same and the distances from the charge(s) to the evaluation point are the same, for both (a) and (b) we have 9 9 2 2 8 10 2 10 [V] 14.1[V] 4 26 4 5 1 C d R ρ π ε π ε π ε-- × × Φ = = = ≈ + ∫ l l 1 Electromagnetics Workshop – Week 9 Solutions Electrostatic Potential and Divergence Theorem Problem 2: A disk, a ρ ≤ ≤ , z = , 2 φ π ≤ ≤ , carries a surface charge density, ( 29 2 2 s s a ρ ρ ρ = . Find ( 29 0,0, V z in free space. Assume ( 29 V ∞ = . Solution: 2 3 2 2 2 0 0 4 4 a s s S dS d d R a z π ρ ρ ρ ρ φ π ε π ε ρ Φ = = + ∫ ∫ ∫ ( 29 3 3 2 2 2 2 2 2 2 2 2 2 2...
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9 - Electromagnetics Workshop – Week 9 Solutions...

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