Method of image with Green function

hubrisos
Homework Statement:
A conducting sphere of radius a is made up of 3 different shells, upper part a/2 \leq z \leq -a/2, the middle part -a/2 \leq z\leq a, the lower part -a \leq z \leq -a/2 where the center of the sphere is at the origin. The upper part V and the lower part has -V potentials, while the mid part is grounded. Find the electric potential at x up to a 4 T order in the expansion of a/x << 1.

Basically the shell has 3 regions, upper, middle, lower. the lower/upper parts are not hemispherical, middle part is relatively broad, and the upper part has V, the lower part has -V potential.
Relevant Equations:
green functions
A conducting sphere of radius a is made up of 3 different shells, upper part a/2
z
-a/2, the middle part -a/2
z
a, the lower part -a
z
-a/2 where the center of the sphere is at the origin. The upper part V and the lower part has -V potentials, while the mid part is grounded. Find the electric potential at x up to
order in the expansion of a/x << 1.

Basically the shell has 3 regions, upper, middle, lower. the lower/upper parts are not hemispherical, middle part is relatively broad, and the upper part has V, the lower part has -V potential.

I don't know where to start, I don't ask you to solve the entire thing, but give me a few tips/hints. I am lost due to the fact that the mid part is huge.

Attachments

• hem.jpg
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Staff Emeritus
Homework Helper
I don't know where to start, I don't ask you to solve the entire thing, but give me a few tips/hints. I am lost due to the fact that the mid part is huge.
Can you be more specific? Why is that throwing you? Your thread title is "Method of image with Green function." That seems to suggest the approach you're supposed to take.

hubrisos
Gee why did not I think of that? Wow such an insight.
Thank you.
What a toxic community...

Staff Emeritus
Homework Helper