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.

 

[vela]

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...

 

[vela]

Well, the rules of the forum are that you need to show some effort, that you actually thought about the problem. "I have no idea where to start" doesn't cut it.

 

[hubrisos]

I did not ask you to solve the whole problem, did I?

I was a member of this website 5-6 years ago, and the same smug attitude was flying around everywhere. it seems it is still the same.

Enjoy your "I know everything" attitude. I am out.

 

[Mark44]

I was a member of this website 5-6 years ago, and the same smug attitude was flying around everywhere. it seems it is still the same.

Our rules are still the same. As @vela said, you need to have shown some effort, at least to the point of thinking about an approach.