Jackson Classical Electrodynamics: Deriving W_{int} from (1.57) to (1.58)

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Discussion Overview

The discussion revolves around the derivation of the interaction energy \( W_{int} \) in Jackson's Classical Electrodynamics, specifically the transition from equation (1.57) to (1.58) in the context of two point charges. The focus is on understanding the mathematical steps involved in this derivation.

Discussion Character

  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests clarification on the derivation process from equation (1.57) to (1.58), noting uncertainty about the substitution mentioned by Jackson.
  • Another participant humorously mentions their reluctance to keep Jackson's book at home, indicating a personal sentiment rather than a technical contribution.
  • A participant points out that some may have earlier editions of Jackson, suggesting that the equation numbering may differ, which could lead to confusion.
  • One participant suggests that the transition is a straightforward substitution and encourages the original poster to post their work for more targeted assistance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specifics of the derivation, and there are varying levels of familiarity with the text and its editions. The discussion remains unresolved regarding the exact steps needed for the derivation.

Contextual Notes

There is a potential limitation regarding the differences in equation numbering across various editions of Jackson's book, which may affect participants' ability to reference the same material.

americanforest
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Can someone explain to me how Jackson, on page 42 of the 3rd ed. of Classical Electrodynamics, when he is deriving the interaction energy [tex]W_{int}[/tex] in his example involving two point charges, gets from equation (1.57) to (1.58). I thought about typing up the TeX but I'm sure most of you have this book. I know he makes that substitution he mentions but I'm not sure how to go about doing that. Help!
 
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I keep my copy of Jackson at the office and not at home. I do not need him to pervade my life any more than is possible.
 
Some of us are old and have earlier editions of Jackson. Presumably the equation numbering is different.
 
It's just a straight substitution: Solve for [itex]\mathbf{x}[/itex] in terms of [itex]\mathbf{\rho}[/itex], and substitute. If you get stuck, post your work and we'll be able to help you better.
 

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