Electrodynamics, Potentials, spherical uncharged shells

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Homework Help Overview

The discussion revolves around finding the electric potential inside an uncharged spherical shell of finite width, which is placed in an electric field directed along the z-axis. The problem involves applying the Laplace principle and utilizing Laplace's equation in a two-dimensional context.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of spherical coordinates for the two-dimensional Laplacian and the separation of variables to derive differential equations. There are attempts to visualize the problem through diagrams, although some participants express difficulty in sharing their visual representations.

Discussion Status

The discussion is ongoing, with some participants providing guidance on the use of boundary conditions and the process of obtaining particular and general solutions. However, there is a lack of explicit consensus on the best approach to take, and multiple interpretations of the problem are being explored.

Contextual Notes

Some participants note the absence of further information related to the problem, which may impact the depth of the discussion. There is also a reminder that tutorial help cannot be provided until participants demonstrate their best efforts.

Dealingwithphysics
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Homework Statement


using Laplace principle find potential inside an uncharged spherical shell of finite width. shell is placed in an electric field E in z-axis direction.

Homework Equations


eq0001M.gif
in this equation u is potential. equation is called 2-D Laplace’s equation.

The Attempt at a Solution


diagram which i picture in my mind is like as under.

[/B]
 

Attachments

  • eq0001M.gif
    eq0001M.gif
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Dealingwithphysics said:

Homework Statement


using Laplace principle find potential inside an uncharged spherical shell of finite width. shell is placed in an electric field E in z-axis direction.

Homework Equations


View attachment 217586 in this equation u is potential. equation is called 2-D Laplace’s equation.

The Attempt at a Solution


diagram which i picture in my mind is like as under.

[/B]
please don't delete i don't have further info related to problem. its it.
 
Dealingwithphysics said:
3. The Attempt at a Solution
diagram which i picture in my mind is like as under.

Dealingwithphysics said:
please don't delete i don't have further info related to problem. its it.
Your image did not Upload correctly. As you know, we cannot provide tutorial help until you show us your best efforts to work the problem. Please try again to Upload a JPEG or PDF image of your work, or just type your work into the forum window using the math symbols under the sigma ∑ symbol, or use LaTeX (see the tutorial under INFO at the top of the page, Help/How-To). Thank you.
 
First is preferably to use spherically coordinates for our two-dimensional
Laplacian. Then you can separate the
variables and actually obtain two different (simple) differential equations.
Upon obeying the Dirichlet boundary conditions you obtain a particular solution depending on an integer.
Then you sum over all values of those
integer numbers in order to obtain a general solution.
so
 

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