Monopole and Dipole moments

  • Thread starter babtridge
  • Start date
  • #1
16
0
I'm having a lot of difficulty calculating the monopole and dipole moments for a dielectric sphere with surface charge of the form,

sigma(theta)=sigma(0)cos(theta)

If surface charge wasn't present and it was just a point charge I would be OK but I need a few pointers on how to do it with the above surface charge density.

Thanks in advance guys........
 

Answers and Replies

  • #2
574
1
What have you tried so far? For arbitary charge densities the moments are

[tex]\int {\rho(\vec{r'}) dV'}[/tex]

and

[tex]\int {\vec{r'}\rho(\vec{r'}) dV'}[/tex]

The monopole moment is just the total charge on the surface. So integrate your surface charge density over the surface of the sphere. For the dipole moment I'm not that sure but I think you have to do the same for [tex]R\sigma(\theta)[/tex] where R is the radius of the sphere. Don't quote me on this though.

edit: change the second intergation over all components of the r vector over the sphere's surface. that would make much more sense than what I previously wrote.
 
Last edited:
  • #3
16
0
Cheers mate,
I was using the multipole expansion formula of phi(r) in spherical polars.
My working matches what you have said so thanks for confirming that!

:rofl:
 

Related Threads on Monopole and Dipole moments

Replies
14
Views
4K
  • Last Post
Replies
2
Views
3K
Replies
13
Views
1K
Replies
1
Views
2K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Top