Density of electric field energy around two surface-charged spheres surrounded by electrolyte II. The smaller sphere is inside the larger one

István P. Sugár; István P. Sugár

doi:10.3934/biophy.2022006

AIMS Biophysics

2022, Volume 9, Issue 1: 61-71. doi: 10.3934/biophy.2022006

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Density of electric field energy around two surface-charged spheres surrounded by electrolyte II. The smaller sphere is inside the larger one

István P. Sugár ^,

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

Received: 20 January 2022 Revised: 27 February 2022 Accepted: 07 March 2022 Published: 18 March 2022

Based on the generalized version of Newton's Shell Theorem [7] the electric field energy density, u_F around two surface-charged spheres surrounded by electrolyte where the smaller sphere is inside the larger one is analytically calculated. According to the calculations when the surfaces of the spheres are farther from each other than four times of the Debye length the field energy density around and inside the smaller sphere is basically independent from the presence of the larger sphere. The electric field energy density is maximal when the smaller sphere touches the inner surface of the larger sphere and the maximum of u_F is located at the touching point on the outer surface of the larger sphere.
- generalized shell theorem,
- electric field energy density,
- Debye length
Citation: István P. Sugár. Density of electric field energy around two surface-charged spheres surrounded by electrolyte II. The smaller sphere is inside the larger one[J]. AIMS Biophysics, 2022, 9(1): 61-71. doi: 10.3934/biophy.2022006

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Abstract

Based on the generalized version of Newton's Shell Theorem [7] the electric field energy density, u_F around two surface-charged spheres surrounded by electrolyte where the smaller sphere is inside the larger one is analytically calculated. According to the calculations when the surfaces of the spheres are farther from each other than four times of the Debye length the field energy density around and inside the smaller sphere is basically independent from the presence of the larger sphere. The electric field energy density is maximal when the smaller sphere touches the inner surface of the larger sphere and the maximum of u_F is located at the touching point on the outer surface of the larger sphere.

Acknowledgments

The author is very thankful for Chinmoy Kumar Ghose.

Conflict of interest

The author declares no conflict of interest.

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