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Unformatted text preview: Electromagnetics Workshop – Week 8 Solutions Electrostatic Potential and Divergence Theorem Problem 1: Given the following electric field, 10 ˆ [V/m], in [m] ρ ρ = Eφ , find the potential difference between the points a ( 29 5 [m], 4 ρ φ π = = and b ( 29 5 [m], ρ φ = = . Use point b as the reference. Solution: [ ] 4 10 5 ˆ ˆ V 2 a ab b d d π π ρ φ ρ Φ =  × =  × =  ∫ ∫ E lφ φ 1 Electromagnetics Workshop – Week 8 Solutions Electrostatic Potential and Divergence Theorem Problem 2: Spherical charge distribution: A spherical charge distribution exists in free space in the region r a ≤ ≤ given by ( 29 2 2 1 r r a ρ ρ = ÷ a) Find the total charge. b) Determine E everywhere. c) Determine Φ everywhere (assume Φ (0)=0). Solution: a) 2 3 2 4 2 2 2 2 0 0 0 8 1 sin 4 15 a a v V a r r Q dV r dr d d r dr a a π π π ρ ρ ρ θ θ φ π ρ = = = = ÷ ÷ ∫ ∫ ∫∫ ∫ b) ˆ encl S dS Q × = ∫∫...
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.
 Fall '08
 Staff
 Electromagnet

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