How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
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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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 .