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How is the boxed step , physically as well as mathematically justified and correct ?


As work done = $- \Delta U $. for Conservative force and it shouldn't matter whether we take $ds$ or $-dr$ ?

And when $dr$ is just a notation to specify the variable and the real thing behind it , is a limit , why is it that $dr$ is so important here .

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Kindly edit my post a bit to prevent linkrot,thank you as I am not able to figure out how to upload images on stack exchange – nonagon Apr 25 '13 at 21:25
Alright , thank you for editing – nonagon Apr 26 '13 at 6:27
and how much reputation you require for uploading images ? – nonagon Apr 26 '13 at 8:48
Cross-posted to – Qmechanic Apr 28 '13 at 14:29
up vote 1 down vote accepted

Basically you $dr$ is negative , so $|dr|=-dr.$ like $|-2|=-(-2)$ , evaluate using this , the sign ambiguity will dissolve .

Also displacements are measured w.r.t. some origin and here , origin can't be placed at $\infty$. So you base your origin at the point where the charge '$Q$' is located .

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