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

  • Thread starter pallab
  • Start date
  • #1
27
2

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?
 

Answers and Replies

  • #2
34,797
10,955
You might want to keep the lowest order that does depend on r. That's what matters for the electric field.
 
  • Like
Likes pallab

Related Threads on Multipole expansion for the case r'>>r and r>>r'

Replies
8
Views
265
  • Last Post
Replies
2
Views
8K
Replies
1
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
4
Views
2K
Top