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## 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?

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?