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Why use primed coordinates for this

  1. Jun 12, 2012 #1
    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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  2. jcsd
  3. Jun 12, 2012 #2

    vanhees71

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    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.
     
  4. Jun 12, 2012 #3
    But why dl'? Is that because you might misinterpret dl unprimed as dl along the vector r (can't find that damn script letter)?
     
  5. Jun 12, 2012 #4
    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'.
     
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