3. Harmonic function in a spherical shell. Find the solution to the Laplace equation in a spherical shell bounded between r = 1 and r = 2 with the following boundary conditions: u|r1 = cos² u|r2 = 2 cos² p =2 where x = r sin ó cos 0, y = r sin ø sin 0, and z = r cos p.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 35E
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3. Harmonic function in a spherical shell. Find the solution to the Laplace equation in a
spherical shell bounded between r = 1 and r = 2 with the following boundary conditions:
u|r1 = cos²
u|r2 = 2 cos² p
=2
where x = r sin ó cos 0, y = r sin ø sin 0, and z = r cos p.
Transcribed Image Text:3. Harmonic function in a spherical shell. Find the solution to the Laplace equation in a spherical shell bounded between r = 1 and r = 2 with the following boundary conditions: u|r1 = cos² u|r2 = 2 cos² p =2 where x = r sin ó cos 0, y = r sin ø sin 0, and z = r cos p.
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