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Problem 3 Consider a capacitor formed by an infinitely large plate on z = 0 with V = 0, and an infinite, solid, conducting cone with an interior angle a/4 held at potential V = Vo. Note that the tip of the cone vertex and the infinitely large plate are insulated. (a) Based on symmetries, explain why V(r, 0, ¢) = V (0) in the space between the cone and the plate. (b) Integrate Laplace's equation explicitly to find the potential between the cone and the plate. (Note that the general solution Eq.(3.65) in Griffiths does not apply to the case here, since we have charges distributed at 0 = T/4 and T/2.)

Problem 3 Consider a capacitor formed by an infinitely large plate on z = 0 with V = 0, and an infinite, solid, conducting cone with an interior angle a/4 held at potential V = Vo. Note that the tip of the cone vertex and the infinitely large plate are insulated. (a) Based on symmetries, explain why V(r, 0, ¢) = V (0) in the space between the cone and the plate. (b) Integrate Laplace's equation explicitly to find the potential between the cone and the plate. (Note that the general solution Eq.(3.65) in Griffiths does not apply to the case here, since we have charges distributed at 0 = T/4 and T/2.)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 3 Consider a capacitor formed by an infinitely large plate on z = 0 with V = 0, and an infinite, solid, conducting cone with an interior angle 7/4 held at potential V = Vo. Note that the tip of the cone vertex and the infinitely large plate are insulated. (a) Based on symmetries, explain why V(r, 0, ø) = V(0) in the space between the cone and the plate. %3D (b) Integrate Laplace's equation explicitly to find the potential between the cone and the plate. (Note that the general solution Eq.(3.65) in Griffiths does not apply to the case here, since we have charges distributed at 0 = 1/4 and T/2.)
Transcribed Image Text:Problem 3 Consider a capacitor formed by an infinitely large plate on z = 0 with V = 0, and an infinite, solid, conducting cone with an interior angle 7/4 held at potential V = Vo. Note that the tip of the cone vertex and the infinitely large plate are insulated. (a) Based on symmetries, explain why V(r, 0, ø) = V(0) in the space between the cone and the plate. %3D (b) Integrate Laplace's equation explicitly to find the potential between the cone and the plate. (Note that the general solution Eq.(3.65) in Griffiths does not apply to the case here, since we have charges distributed at 0 = 1/4 and T/2.)
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