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

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The discussion centers on deriving the interaction energy W_{int} in Jackson's Classical Electrodynamics, specifically transitioning from equation (1.57) to (1.58). Participants clarify that the key step involves substituting variables by solving for \mathbf{x} in terms of \mathbf{\rho}. There is an acknowledgment that different editions of the book may have varying equation numbers, which could lead to confusion. Users are encouraged to share their work if they encounter difficulties for more tailored assistance. Overall, the focus is on understanding the substitution process in the derivation.
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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 W_{int} 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 \mathbf{x} in terms of \mathbf{\rho}, and substitute. If you get stuck, post your work and we'll be able to help you better.
 
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