The discussion focuses on deriving the potential energy of an electron inside a uniformly charged nucleus, represented by the equation V'(r) = (-Ze²/4πε₀R)(3/2 - (1/2)(r/R)²). Participants emphasize the importance of correctly applying integration limits and verifying that the electric field behaves as expected within the nucleus. The electric field inside a homogeneously charged sphere is confirmed to be proportional to the radius, and the Shell Theorem is suggested as a mathematical tool to aid in the derivation.
PREREQUISITESStudents and educators in physics, particularly those focusing on electrostatics, as well as anyone involved in deriving equations related to electric fields and potential energy in charged systems.
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.