- #1
ligneox
- 2
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- Homework Statement
- The surface depicted in the image below is constructed from three parts: (1) An outer hemispherical shell of radius ๐; (2) an inner hemispherical shell of radius ๐; and (3) a flat bottom that sits in the ๐ฅ โ ๐ฆ plane. The potential on each of the three surfaces is specified
as ๐1(๐, ๐) = 0, ๐2(๐, ๐) = 5๐0 cos ๐ sin^2๐, and ๐3(๐, ๐โ2) = 0. Here ๐0 is a constant and ๐, ๐ are the usual spherical coordinates. Find the electric potential in the hemispherical shell ๐ โค ๐ โค ๐.
- Relevant Equations
- V(r,๐) = sum n=0 to infinity (A_n r^n + B_n/(r^(n+1))) P_n(cos๐)
I'm having troubles setting up this problem. I know we are to use boundary conditions to determine An and Bn since in this case (a<r<b) neither can be set to 0. I don't know how the given potentials translate into boundary conditions, especially the V3 disk.