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
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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
Transcribed Image Text: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(Ør)
on the boundary.
c) Find the total charge induced on the knob.
P(r)
a
b
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