Question: A capacitor is formed by the infinite grounded plane z = 0 and an infinite, solid, conducting cone with interior angle /4 held at potential

A capacitor is formed by the infinite grounded plane z = 0 and an infinite, solid, conducting cone with interior angle π/4 held at potential V. A tiny insulating spot at the cone vertex (the origin of coordinates) isolates the two conductors. p = V p=0 4

(a) Explain why φ(r, θ, φ) = φ(θ) in the space between the capacitor “plates”.
(b) Integrate Laplace’s equation explicitly to find the potential between the plates.

p = V p=0 4

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