Problem 3Consider a capacitor formed by an infinitely large plate on z = 0 withV = 0, and an infinite, solid, conducting cone with an interior angle 7/4held at potential V = Vo. Note that the tip of the cone vertex and theinfinitely large plate are insulated.(a) Based on symmetries, explain why V(r, 0, ø) = V(0) in the spacebetween the cone and the plate.%3D(b) Integrate Laplace's equation explicitly to find the potential betweenthe cone and the plate. (Note that the general solution Eq.(3.65)in Griffiths does not apply to the case here, since we have chargesdistributed at 0 = 1/4 and T/2.)

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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.)

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.1P: Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius r0. Both of...

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