Why use primed coordinates for this

aaaa202

Griffiths notation kind of bothers me. Can anyone explain why he uses primed coordinates in the attached picture. Wouldn't dl, da, dτ do just as well?
Cheers :)

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vanhees71

I hate books that are so sloppy in their notation :-(. What he wants to write is

[tex]\Phi(\vec{x})=\int \mathrm{d}^3 \vec{x}' \frac{\rho(\vec{x}')}{4 \pi |\vec{x}-\vec{x}'|},[/tex]

which gives the electrostatic potential of a (time independent!) charge distribution [itex]\rho[/itex] (in Heaviside-Lorentz units). Note that there are two points involved: First there's the point [itex]\vec{x}[/itex] at which the potential is calculated and the point [itex]\vec{x}'[/itex] which is at the location of a charge [itex]\rho(\vec{x}') \mathrm{d}^3 \vec{x}'[/itex]. Then you "sum" (integrate) over all these charge elements.

zezima1

But why dl'? Is that because you might misinterpret dl unprimed as dl along the vector r (can't find that damn script letter)?

Hassan2

You integrate over primed coordinates so the integration element ( dl') is primed too. In vanhees71's notation, d³x' is an infinitesimal volume at point x'. For the 1D case, dl' is an infinitesimal length at point r'.