How Does Lightning Affect Lattice Behavior in Macroscopic Theory?

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Discussion Overview

The discussion revolves around the effects of lightning on lattice behavior within the framework of macroscopic theory. Participants explore concepts related to energy density in electric fields, particularly in the context of Gaussian units and time-averaged values.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the relationship between optical power and the average of the electric field squared, referencing a specific passage.
  • Another participant questions the initial claim, suggesting that the energy density of an electric field is typically half of what was stated, providing formulas in both SI and Gaussian units.
  • A participant acknowledges the use of Gaussian units and attempts to reconcile the differences in constants mentioned, indicating a potential misunderstanding of energy density versus time-averaged values.
  • There is a suggestion that the Poynting vector may be relevant to the discussion, although its role is not clearly defined.
  • One participant introduces the concept of root mean square (RMS) electric field values, indicating a potential complication in the calculations presented.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of energy density in electric fields, with no consensus reached on the interpretation of the original passage or the implications of RMS values.

Contextual Notes

There are unresolved mathematical steps and potential dependencies on definitions, particularly regarding the treatment of energy density in different unit systems and the implications of time-averaging in the context of wave behavior.

armandowww
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I was searching for some proof on macroscopical theory about lattice behaviour under lightning. I found a passage in which the average in time of optical power is given by average of electrical field square times constant dielectric ratio four pi! How could I explain this concept?
Regards
 
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I'm not sure I understand what you are talking about - it would help if you provided a reference or link to the passage.

In general, the energy density of an electric field is half the number you stated.

[tex]\frac{d{\cal E}}{dV} = \frac{1}{2} \epsilon E^2~~(SI~Units)[/tex]

[tex]\frac{d{\cal E}}{dV} = \frac{1}{8\pi} \epsilon_r E^2~~(Gaussian~Units)[/tex]
 
I've just forgot to say you I'm in gaussian units... but your 8 is my 4
 
Mayhap... the reason is this: you told about an energy density at a given instant, while the time average of my waves (PLANE waves) has brought new root-square-two terms (2 terms because E is the base of a power 2) forward in my formula...
Is the Poynting vector involved in anyway?
Thank you
 
[tex]E_{RMS} = \frac{E_0}{\sqrt{2}}[/tex]

That would only make things worse.

[tex]\frac{d{\cal E}}{dV} = \frac{1}{8\pi} \epsilon_r E_{RMS}^2 = \frac{1}{16\pi} \epsilon_r E_0^2[/tex]
 

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