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 :)

 

[vanhees71]

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

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

which gives the electrostatic potential of a (time independent!) charge distribution $\rho$ (in Heaviside-Lorentz units). Note that there are two points involved: First there's the point $\vec{x}$ at which the potential is calculated and the point $\vec{x}'$ which is at the location of a charge $\rho(\vec{x}') \mathrm{d}^3 \vec{x}'$. 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]

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

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'.