Week 8 Solns - Electromagnetics Workshop Week 8 Solutions...

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Electromagnetics Workshop – Week 8 Solutions Electrostatic Potential 1 Problem 1: Given the following electric field, 10 ˆ [V/m], in [m] ρ = E φ , find the potential difference between the points a ( ) 5[m], 4 ρφ π == and b () 0 . Use point b as the reference. Solution: [] 4 0 10 5 ˆˆ V 2 a ab b dd Φ= − ⋅ = = ∫∫ El φφ
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Electromagnetics Workshop – Week 8 Solutions Electrostatic Potential 2 Problem 2: Spherical charge distribution: A spherical charge distribution exists in free space in the region 0 ra ≤≤ given by () 2 0 2 1 r r a ρρ ⎛⎞ =− ⎜⎟ ⎝⎠ a) Find the total charge. b) Determine E everywhere. c) Determine Φ everywhere (assume Φ (0)=0). Solution: a) 2 3 24 22 0 00 000 0 8 1s i n 4 15 aa v V a rr Qd V rd r d d r d r ππ πρ θ φ π ρ == = = ∫∫ b) ˆ encl S dS Q ⋅= Dn w 35 2 0 2 44 r Dr a 2 0 2 0 1 r Er a a ε 3 2 0 8 4 15 r a = 3 0 2 0 2 15 r a a r = c) a b d Φ=− El 2 0 2 0 0 1 r dr a 2 2 0 2 0 1 21 0 3 r r a Φ= 3 2 0 2 1 1 5 ar a r dr dr εε 2 0 0 15 4 r
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Electromagnetics Workshop – Week 8 March 24, 2006 Electrostatic Potential 3 Problem 3: Find the electrostatic potential at (0, 0, 5) [m] in air produced by: a) 8 [nC] distributed as a uniform ring of charge at 0 z = , 1 ρ = [m]; b) four point charges, 2 [nC] each, at ( ± 1, 0, 0) [m] and (0, ± 1, 0) [m].
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Week 8 Solns - Electromagnetics Workshop Week 8 Solutions...

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