A generalization of the Shell Theorem.<br/>Electric potential of charged spheres and charged vesicles surrounded by electrolyte

István P. Sugár; István P. Sugár

doi:10.3934/biophy.2020007

AIMS Biophysics

2020, Volume 7, Issue 2: 76-89. doi: 10.3934/biophy.2020007

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A generalization of the Shell Theorem.
Electric potential of charged spheres and charged vesicles surrounded by electrolyte

István P. Sugár ^,

Department of Neurology, Icahn School of Medicine at Mount Sinai, New York, NY 10029

Received: 31 January 2020 Accepted: 10 April 2020 Published: 15 April 2020

By using the screened Coulomb potential a generalized version of Newton's Shell Theorem is developed and analytical equations are derived to calculate i) the potential of a charged sphere surrounded by electrolyte, ii) the potential of two concentric charged spheres surrounded by electrolyte, and iii) the potential inside the membrane of a charged lipid vesicle surrounded by electrolyte with high ion concentration. By numerical integration the potential of a lipid vesicle is calculated at any electrolyte concentration.
- membrane potential,
- Debye-Hückel equation,
- screened potential,
- Debye length
Citation: István P. Sugár. A generalization of the Shell Theorem.Electric potential of charged spheres and charged vesicles surrounded by electrolyte[J]. AIMS Biophysics, 2020, 7(2): 76-89. doi: 10.3934/biophy.2020007

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Abstract

By using the screened Coulomb potential a generalized version of Newton's Shell Theorem is developed and analytical equations are derived to calculate i) the potential of a charged sphere surrounded by electrolyte, ii) the potential of two concentric charged spheres surrounded by electrolyte, and iii) the potential inside the membrane of a charged lipid vesicle surrounded by electrolyte with high ion concentration. By numerical integration the potential of a lipid vesicle is calculated at any electrolyte concentration.

Acknowledgments

The author is very thankful for Chinmoy Kumar Ghose.

Conflict of interest

The author declare no conflict of interest.

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