## Abstract

By using the recently generalized version of Newton’s Shell Theorem [6] analytical equations are derived to calculate the electric potential energy needed to build up a charged sphere, and the field and polarization energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the electrolyte’s ion concentration and the radius of the charged sphere. The work needed to build up the charged sphere, E_{cc} (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the electrolyte ions’ increasing screening effect on the charge-charge interaction. The work needed to build up the charged sphere appears as a sum of the field and polarization energy of the electrolyte. At zero ion concentration the electrolyte’s field energy is equal with E_{cc} while the polarization energy is zero. At high electrolyte ion concentrations (C>10mol/m^{3}) 50% of E_{cc} appears as the polarization energy of the electrolyte, 25% as the electrolyte’s field energy inside the sphere and 25% as the electrolyte’s field energy around the sphere.

Original language | English |
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Pages (from-to) | 157-164 |

Number of pages | 8 |

Journal | AIMS Biophysics |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - 2021 |

## Keywords

- Debye length
- charge-charge interaction energy
- electrolyte’s field energy
- screened potential