Question

What is the minimal number of point charges required to model an electric octupole?

Answer 1

In an answer to this question, I showed that a general electric quadrupole can be modeled by a combination of seven point charges (or possibly less if one or two of the principal quadrupole moments is zero, or if they add to zero). This is likely the minimal number, or at least it is likely to be the minimal systematic expansion (or, if it isn't, I'll be happy to be corrected).

However, that construction strongly relies on the diagonalization of the quadrupole moment matrix, so it does not easily generalize to higher orders of the multipole tensor hierarchy.

Thus, I would like to ask: given an arbitrary electric octupole moment tensor QijkQijk, what is the minimal number of point charges for which the leading term in the multipole expansion will be precisely that octupole term? (More technically, I'm looking for a systematic procedure that will take an octupole moment tensor QijkQijk and produce a collection of point charges {qi,ri}Ni=1{qi,ri}i=1N, where NN is minimal across all QijkQijk.)

I would expect the answer to this question to hinge on the ways one can analyze and simplify tensors of rank 3 and higher. (As an example of what I mean, the quadrupole moment tensor for two point charges +q+q at ±de^±de^ and a point charge −2q−2q at the origin has all-nonzero components unless e^e^falls on a coordinate plane, even though the minimal model is much simpler than that. Moving to the principal-moments frame strips away this unnecessary complexity.) I am mostly interested in those tools to analyse and understand the general case, rather than some abstruse mathsy way to pare down the number of charges in some weird edge case.

Answer 2

Hello Friend..❤️❤️

The answer of u r question is..✌️✌️

What is the minimum number of point charges required to model and electric octuple??

Ans:✍️✍️✍️✍️✍️✍️✍️

I showed that electric after fall B model by combination of seven point charges for possibly less if one or two of the principal quadrupole moment is zero or if the at 20 this is likely the minimum number or at least it is likely to B model by combination of seven point charges for possibly less if one or two of the principal quadrupole moment is zero or if the at 20 this is likely the minimum number or at least it is likely to be minimal.


Thank you..⭐️⭐️⭐️