The discussion revolves around deriving the potential energy of an electron within a nucleus, modeled as a uniformly charged sphere. The specific equation in question relates to the potential energy as a function of the distance from the center of the nucleus.
The discussion is active, with participants providing guidance on checking the consistency of the derived formula with known physical principles, such as the shell theorem. There is an ongoing exploration of the mathematical derivation needed to reach the desired formula.
Participants are navigating the complexities of electric field behavior within a charged sphere and the implications for potential energy calculations. There is an emphasis on ensuring that the derived equations align with established physical laws.
First, Electrical field is not linearly dependent on distance! And I am not trying to find the field at the nucleus border but inside it. Can you help please to reach the desired formula?mfb said:Something went wrong with the formatting.
The electric field should be linear with the distance - right. You can check if the electric field at the border of the nucleus agrees with the electric field of a point-charge. If yes, your result is right.
Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.haseeb said:Electrical field is not linearly dependent on distance!
Yup! You are right... But How to drive it mathematically?mfb said:Inside a homogeneously charged sphere, it is proportional to the radius, its magnitude is proportional to the distance to the center.
If your formula reproduces this relationship and agrees at the boundary, then it is right. Hence the suggestion to check if it fits at the boundary.