Spherical layer charge distribution and multipole expansion

In summary, the conversation discusses using the multipole expansion method to calculate the electrostatic potential of a random spherical distribution of charges between two radii, which is a faster and more efficient approach compared to explicit calculation. The person asks for recommendations on references or examples for similar calculations and is directed to check out fastmultipole.org, specifically their tutorial section.
  • #1
Horacius.Rex
1
0
Hi,

I have a random spherical distribution of N charges between radiuses
R1 and R2. N is up to 10^9 or more.I want to calculate the
electrostatic potential closed to the origin of the sphere. R1 and R2
are much bigger than the distance of this point to the origin. So I
thought about using the multipole expansion to calculate the
potential, because it is supposed to reduce the Tcpu a lot, mainly
because in this approach Tcpu proportional to N, and in explicit
electrostatical potential calculation Tcpu proportional to N^2. So,
could you recommendme references in good books or papers or weblinks
with examples of similar calculations ?

Thanks
 
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  • #2

1. What is a spherical layer charge distribution?

A spherical layer charge distribution refers to a scenario where electric charges are distributed uniformly on the surface of a spherical shell.

2. Why is spherical layer charge distribution important in multipole expansion?

Spherical layer charge distribution is important in multipole expansion because it provides a convenient and efficient way to describe the electric potential and electric field of a charge distribution. It also allows for simplification of complex charge distributions into simpler, multipole terms.

3. How is the multipole expansion of a spherical layer charge distribution calculated?

The multipole expansion of a spherical layer charge distribution is calculated by using the Legendre polynomials and the spherical harmonics functions. These functions are used to express the potential and electric field in terms of multipole moments, which are related to the charge distribution.

4. What is the difference between a monopole and a dipole in the multipole expansion of a spherical layer charge distribution?

A monopole term in multipole expansion refers to a single point charge at the center of the spherical shell, while a dipole term refers to two equal and opposite charges located on the opposite sides of the spherical shell.

5. How does the number of terms in the multipole expansion of a spherical layer charge distribution affect the accuracy of the calculation?

The more terms included in the multipole expansion, the more accurate the calculation will be. However, including too many terms can also lead to computational errors. Therefore, a balance must be struck between accuracy and efficiency in choosing the number of terms in the expansion.

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