# Why charges go to the surface: A generalized Thomson problem

@article{Levin2003WhyCG, title={Why charges go to the surface: A generalized Thomson problem}, author={Yan Levin and Jeferson J. Arenzon}, journal={EPL}, year={2003}, volume={63}, pages={415-418} }

We study a variant of the generalized Thomson problem in which n particles are confined to a neutral sphere and interacting by a 1/rγ potential. It is found that for γ ≤ 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However, for γ > 1 and n > nc(γ) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes.

## Figures from this paper

## 27 Citations

Two and three electrons on a sphere: A generalized Thomson problem

- PhysicsPhysical Review B
- 2018

Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate…

Electromagnetic instability of the Thomson problem

- Physics
- 2005

The classical Thomson problem of n charged particles confined to the surface of a sphere of radius a is analyzed within the Darwin approximation of electrodynamics. For n nc(a) the Wigner lattice is…

On the connected-charges Thomson problem

- Physics
- 2006

We investigate the modifications brought about by the linear connectivity among charges in the classical Thomson problem. Instead of packing with local hexagonal order interspersed with topological…

Probing infinity in bounded two-dimensional electrostatic systems.

- PhysicsChaos
- 2016

This work considers fractals to be physical entities, with charges located in their vertices or nodes, and describes how energy diverges at charge accumulation points in the fractal, that is, almost everywhere by definition.

Charge reversal at 0 K

- Physics
- 2004

In this contribution we shall explore the conditions under which a charged sphere in contact with a charge reservoir undergoes a charge reversal. The calculations are confined to zero temperature,…

Numerical Study of the Structure of Metastable Configurations for the Thomson Problem

- Mathematics
- 2016

A numerical method is proposed for solving the Thomson problem – finding stable positions for a system of N point charges distributed on a sphere that minimize the potential energy of the system. The…

The Structure of Metastable States in The Thomson Problem

- Mathematics
- 2015

A practical numerical method for the effective solution of the Thomson Problem is proposed. The developed iterative algorithm allows to conduct theoretical researches such as study of the number of…

Electrostatics in soft matter.

- Physics, ChemistryJournal of physics. Condensed matter : an Institute of Physics journal
- 2009

Recent progress in understanding the effect of electrostatics in soft matter is presented, and theoretical and simulational aspects, including the experimental motivations, will be discussed.

## References

SHOWING 1-10 OF 19 REFERENCES

Crystalline order on a sphere and the generalized Thomson problem.

- PhysicsPhysical review letters
- 2002

Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures.

MATH

- Biology
- 1992

It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.

I

- EngineeringEdinburgh Medical and Surgical Journal
- 1824

AIV Assembly, Integration, Verification AOA Angle of Attack CAD Computer Aided Design CFD Computational Fluid Dynamics GLOW Gross Lift-Off Mass GNC Guidance Navigation and Control IR Infra-Red LEO…

Phys

- Rev. Lett. 89, 185502
- 2002

Phys. Rev. Lett

- Phys. Rev. Lett
- 2002

Rep

- Prog. Phys. 65, 1577
- 2002

Rep. Prog. Phys

- Rep. Prog. Phys
- 2002

Phys

- Rev. E 64, 021405
- 2001

Phys. Rev. E

- Phys. Rev. E
- 2001

Phys

- Rev. E 60, 5802
- 1999