Two hemispheres, and a shell inside dielectric material

In summary, the conversation discusses two questions related to spherical shells with different charge densities. The first question is solved using direct integration, but the lack of symmetry in the space makes it difficult to solve on a specific axis. The second question is solved using separation of variables, but there is uncertainty about the potential inside the shell.
  • #1
Phylosopher
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Hello,I am trying to solve two different questions, and I am having trouble finding the solution:

1- Spherical shell of radius R, have two hemispheres of different charge density. The northerns hemisphere is +σ and the southern hemisphere is -σ. Use direct integration to find V inside and outside the shell. (i.e V=k∫σ'/χ dr').

2- A spherical shell of radius a that have charge density of σcos(θ) is placed in a dielectric material that surround it and makes spherical shape around it with radius b. Find V in the whole space using separation of variables.[i.e shell of radius a attached from the inside to a dielectric material of radius a to b]For (1), I solved it using separation of variables, and it does give me a series. The problem with direct integration is that there is no symmetry in the space so I cannot solve the problem on specific axis! more than that, I have no idea how to solve the problem inside the sphere.

For (2), I did solve the question but I am wondering, is the potential inside the shell is constant or not?
 
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  • #2
I tried to be as clear and simple as possible. If anyone can help and didn't get fully what I wrote or my post seems vague, please comment.
 

FAQ: Two hemispheres, and a shell inside dielectric material

1. What are two hemispheres in the context of dielectric material?

The two hemispheres refer to the two halves or sections of the dielectric material that surround the shell inside.

2. How is a shell inside dielectric material significant?

A shell inside dielectric material is significant because it creates a boundary between the two hemispheres, allowing for the accumulation of electric charge on either side.

3. What is the role of the dielectric material in this concept?

The dielectric material serves as an insulator between the two hemispheres, preventing the flow of electric current and allowing for the accumulation of charge on either side of the shell.

4. Can a shell inside dielectric material hold a charge?

Yes, a shell inside dielectric material can hold a charge. The insulating properties of the dielectric material prevent the charge from dissipating, resulting in a build-up of electric charge on either side of the shell.

5. What applications does this concept have in the field of science?

This concept has many applications in science, particularly in the study of electricity and electromagnetism. It can also be applied in the development of capacitors, which use a similar design to store electric charge.

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