Griffith's ED Chapter 4 Clarification (Bound Charges)

[Jason Williams]

I'm having an issue with the equation that Griffith uses to derive the field of a polarized object. In Chapter 4, Section 2.1, he starts off with equation 4.8 with the 'script r' to denote the distance between a point outside the distribution P (and the origin) and the dipole (and the origin). He references equation 3.99 to 'derive' this, but equation 3.99 is the field from a dipole and only depends on the distance from the origin to the point P. I don't quite understand how he makes this jump.

 

[MaxwellsCat]

I think he's using script r to denote distance from the dipole to the point in question because he's no longer dealing with distances far from the dipole where r and script r are basically equivalent.

 

[Jason Williams]

Okay that's what I figured, but is it fair just to make that substitution? Like why not use the regular equation for the potential?

 

[MaxwellsCat]

I mean they're equivalent except for the definition of distance that you use. Technically the one with script r is more correct I think, but for distances far from the dipole you approximate with r.

The equation is an approximation anyway, but there are orders of correctness I guess.

 

[Jason Williams]

Okay cool, got it. Thanks so much!