Chapter 7 drill
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This document provides solutions to drill problems from Chapter 7 of the textbook Engineering Electromagnetics by William Hyatt, 7th Edition. The solutions include calculating electric fields and potentials given Laplace's equations. Key steps like taking derivatives and applying boundary conditions are shown. Diagrams assist with visualizing iterative methods for solving problems.
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Chapter 7 drill
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- 3. 1 CHAPTER 7 DRILLS D7.1 (a) V |P (1,2,3) = 4(2)(3) (1)2 +1 = 12 V As, ρv = −∇2 V, so we first calculate ∇2 V : ∇V = −8 yzx (x2 +1)2 + 4z x2 +1 + 4y x2 +1 ⇒ ∇2 V = 32 yzx2 (x2 +1)3 −8 yz (x2 +1)2 ⇒ ∇2 V |P (1,2,3) = 12; so, ρv = −∇2 V = −o(12) = −106.25pC m3 (b) V | P (3, π 3 ,2) = − 22.5 V As, ρv = −∇2 V, so we first calculate ∇2 V : ∇2 V = 20 cos (2φ) −20 cos(2 φ) ⇒ ∇2 V |P (3, π 3 ,2) = 0; so, ρv = −∇2 V = −o(0) = 0 pC m3 Solved by Zaeem Ahm ad Vara ich Com piled by www.EngineersTeam.tk
- 4. (c) V |P (0.5,45o ,60o ) = 4 V As, ρv = −∇2 V, so we first calculate ∇2 V : ∇2 V = 4 cos(φ) r4 −2 cos(φ) r4 (sin(θ))2 ⇒ ∇2 V |P (0.5,45o ,60o ) = 0; so, ρv = −∇2 V = −o(0) = 0 pC m3 D7.2 Apply the formulae & concepts to find the answers! www.engineersteam.tk Compiled by www.EngineersTeam.tk 2 D7.3 (a) The solution to Laplace’s equation 1 ρ ∂ ∂ρ ρ ∂ ∂ρ = 0 is: V = A ln ρ + B Putting the given values of V & ρ and solving the simultaneous equations, we get: A = −73.9 & B = 101.28 so, V = −73.9 ln ρ + 101.28 1 1 Compiled by www.EngineersTeam.tk
- 5. Link 3 of 4 Now, E = −∇V = ρ (73.9) aρ = √ 10 (73.9) aρ = 23.36aφ ( ∵ ρ = √ 3 2 + 1 2 ) so, |E| = 23.36 V m (b) The solution to Laplace’s equation 1 ρ2 ∂2 V ∂φ2 = 0 is: V = Aφ + B Putting the given values of V & φ and solving the simultaneous equations, we get: A = −85.9 & B = 64.9 so, V = −85.9φ + 64.9 Now, E = −∇V = 1 ρ (85.9) aφ = 1√ 10 (85.9) aφ = 27.16 aφ (∵ ρ = √32 + 12) so, |E| = 27.16 V m D7.4 & D7.5 Not included in the course! www.engineersteam.tk Compiled by www.EngineersTeam.tk
- 6. 3 D7.6 The solution to this problem depends on how you proceed in each iteration and on your initial estimate. The dotted lines show how the initial estimate was found. (a) 20.8 V (b) 44.47 V (c) 89.8 V Compiled by www.EngineersTeam.tk Search This Document Search Search History: Searching... Result 00 of 00 00 results for result for p.
- 7. Www.engineersTeam.tk-chapter 7-Engineering Electromagnetics by William Hyatt 7th-Edition-DRILL PROBLEMS SOLUTION- Www.engineersTeam.tk Add To Collection 86 Reads 0 Readcasts 0 Embed Views This is a private document. Published by www.engineersteam.tk Compiled by www.EngineersTeam.tk
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