Monopole and Dipole moments

In summary, the conversation discusses the difficulty in calculating the monopole and dipole moments for a dielectric sphere with a surface charge of the form sigma(theta)=sigma(0)cos(theta). The monopole moment can be found by integrating the surface charge density over the surface of the sphere, while the dipole moment involves integrating R*sigma(theta) over all components of the r vector on the sphere's surface. The speaker also mentions using the multipole expansion formula in spherical polars and confirms that their working matches with the suggested method.
  • #1
babtridge
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...
 
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  • #2
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
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!

:smile:
 

Related to Monopole and Dipole moments

1. What is a monopole moment?

A monopole moment refers to the moment of a single charge or a distribution of charges that do not cancel out. It is also known as a pure electric moment.

2. How is a dipole moment calculated?

A dipole moment is calculated by multiplying the magnitude of the charge by the distance between the two charges and the direction of the vector connecting the two charges.

3. What is the significance of dipole moments in chemistry?

Dipole moments play a crucial role in understanding the polarity of molecules. They help determine the overall distribution of charge within a molecule, which affects its physical and chemical properties.

4. Can a molecule have a non-zero dipole moment even if it is symmetrical?

Yes, a molecule can have a non-zero dipole moment even if it is symmetrical. This is because the dipole moment takes into account both the magnitude and direction of the charges, not just their spatial arrangement.

5. How do monopole and dipole moments differ?

A monopole moment involves a single charge, whereas a dipole moment involves two opposite charges. Additionally, monopole moments have no direction, while dipole moments have a specific direction along the line connecting the two charges.

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