Multipole expansion for the case r'>>r and r>>r'

[pallab]

Homework Statement

what is the multipole expansion of a charge q for two extreme cases r>>r' and r'>> r?

Relevant Equations

1/R=(1/r)* [ summation (r'/r)^nPn(cos a)]

for the case, r>>r' the higher-order term like 1/r^2 and above that is negligible.
so V(r)=cons.*1/r*P0(cos a)
but for the case r'>>r will it be V(r)=cons.*1/r'[ summation Pn(cos a')t'^n] where t'=r/r'
now if we neglect higher-order term of r/r' then V(r)=cons.*1/r'*P0(cos a') which is constant not a function of r.
is it correct? what is the physics behind it?

 

[mfb]

You might want to keep the lowest order that does depend on r. That's what matters for the electric field.