Consider the configuration shown in the figure: An in- finite plane conductor has a small hemispherical knob of radius a as indicated. A point charge q is placed directly to the right hand side of the hemispherical knob at a distance b from its center. Assume that the boundary, i.e. the infinite plane with the knob, is kept at zero potential. a) Find the potential p at a generic point P on the right hand side. b) Determine the appropriate Dirichlet Green function for this geometry and write down the most general solution of the potential p given a generic charge density p on the right hand side of the boundary and that potential p = f("r) on the boundary. %3D c) Find the total charge induced on the knob. P(r) a b

Consider the configuration shown in the figure: An in- finite plane conductor has a small hemispherical knob of radius a as indicated. A point charge q is placed directly to the right hand side of the hemispherical knob at a distance b from its center. Assume that the boundary, i.e. the infinite plane with the knob, is kept at zero potential. a) Find the potential p at a generic point P on the right hand side. b) Determine the appropriate Dirichlet Green function for this geometry and write down the most general solution of the potential p given a generic charge density p on the right hand side of the boundary and that potential p = f("r) on the boundary. %3D c) Find the total charge induced on the knob. P(r) a b

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter4: Transmission Line Parameters

Section: Chapter Questions

Problem 4.4P: One thousand circular mils or 1 kcmil is sometimes designated by the abbreviation MCM75C. Data for...

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