Discussion Overview
The discussion revolves around the energy density of an electromagnetic field in the context of linear dielectrics. Participants explore the relationship between macroscopic and microscopic electrodynamics, and the implications of integrating over free versus bound charges.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions whether the first result for energy density neglects the energy from bound charge and seeks clarification on why certain formulae break down in the presence of dielectrics.
- Another participant asserts that the energy density expression for macroscopic electrodynamics is correct and references Markovian linear-response theory to explain the relationship between the electric displacement field and the electric field.
- A third participant suggests consulting Griffith's Electrodynamics for further discussion on energy in dielectric systems, pointing to specific sections for reference.
- A later reply indicates that the previous explanations have clarified the initial confusion regarding the topic.
Areas of Agreement / Disagreement
Participants do not reach a consensus, as there are differing views on the treatment of bound charges and the applicability of certain equations in the context of dielectrics.
Contextual Notes
There are limitations regarding the integration of free and bound charges, as well as the assumptions made in transitioning between macroscopic and microscopic frameworks, which remain unresolved.
. It is also known that energy can be found by
. Using the latter, the energy density is found to be
, as is well known. If you integrate the latter only over free charge and ignore bound charge, you write
, use integration by parts, and obtain the first result. Does the first result neglect the energy from bound charge? If not, why does
break down (I.e. why can’t one find the energy with a dielectric by treating the bound charge as its own independent charge arrangement and using formulae for a vacuum?)
