Related Experiment Video
Updated: Apr 15, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Coulomb energy of uniformly charged spheroidal shell systems
Vikram Jadhao1, Zhenwei Yao1, Creighton K Thomas1
1Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Abstract:
We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.
More Related Videos
10:38Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis
Published on: September 3, 2013
10:10Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
Published on: December 4, 2020
Related Concept Videos
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Gauss's Law: Spherical Symmetry
The Energies of Atomic Orbitals
Coulomb's Law
Newton's third law applies to the Coulomb force — the...
Gravitation Between Spherically Symmetric Masses
Energy Associated With a Charge Distribution