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10 - Electromagnetics Workshop Week 10 Solutions...

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Electromagnetics Workshop – Week 10 Solutions Electrostatic Potential, Dielectrics, & Faraday’s Law Problem 1: An infinitely long cylindrical shell of uniform charge density 0 s ρ [C/m 2 ] is shown below. a) Calculate the potential inside the shell, by integrating the electric field. Assume that the potential is zero on the z -axis. b) Calculate the potential outside the shell, by integrating the electric field. Assume again that the potential is zero on the z -axis. c) Modify your answers to the above two parts to obtain the solutions if the potential on the z -axis is 10 [V]. : 0 a ρ < = E , no charge is enclosed [ ] 0 0 : V/m s a a ρ ρ ε ρ = E : 0 a ρ < Φ = , since the electric field is zero inside ( 29 [ ] 0 0 0 0 : ln V s s a a a a a d ρ ρ ρ ρ ρ ρ ε ρ ε ρ Φ = - = ÷ If the potential on the z-axis is 10 [V]: : 0 a ρ < = E , no charge is enclosed [ ] 0 0 : V/m s a a ρ ρ ε ρ = E [ ] : 10 V a ρ < Φ = , since the electric field is zero inside ( 29 ( 29 ( 29 [ ] 0 0 0 0 : 0 ln 10 V s s a a a a a d ρ ρ ρ ρ ρ ρ ρ ε ρ ε ρ Φ - Φ = - Φ = + ÷ 1
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Electromagnetics Workshop – Week 10 Solutions Electrostatic Potential, Dielectrics, & Faraday’s Law Problem 2: Fused silica (SiO 2 ) has a relative permittivity of approximately 3.8. The density of fused silica is 2.2 [g/cm 3 ]. There are 21.44352×10 24 molecules per kg of fused silica. (This comes from assuming an atomic mass of 28.0855, so that one mole of fused silica equals 28.0855 grams. A
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