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Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Coulomb's Law01:30

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
Newton's third law applies to the Coulomb force — the force on...
Comparison Between Electrical And Gravitational Forces01:24

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To compare the numerical strengths of the first two, take two particles of the same kind. Since electrons are fundamental particles, they are a good example.
Since both are inverse square law forces, the distance gets canceled when the ratio of the two forces is considered. Instead, the ratio of the electrical and gravitational forces depends on...
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Electric Field of Two Equal and Opposite Charges01:30

Electric Field of Two Equal and Opposite Charges

Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
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Updated: May 8, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Electrostatic forces in the Poisson-Boltzmann systems.

Li Xiao1, Qin Cai, Xiang Ye

  • 1Department of Biomedical Engineering, University of California, Irvine, California 92697, USA.

The Journal of Chemical Physics
|September 14, 2013
PubMed
Summary
This summary is machine-generated.

This study presents a new method for calculating electrostatic forces in biomolecular simulations. The derived Maxwell stress tensor offers a more robust approach for nonlinear Poisson-Boltzmann models, improving accuracy in molecular mechanics.

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Area of Science:

  • Computational Biology
  • Theoretical Chemistry
  • Biophysics

Background:

  • Continuum electrostatic modeling via Poisson-Boltzmann equation is crucial for biomolecular analysis.
  • Integrating these models into molecular mechanics is challenging due to difficulties in assigning atomic forces.

Purpose of the Study:

  • To derive analytical electrostatic forces from the Maxwell stress tensor for nonlinear Poisson-Boltzmann equations.
  • To establish a more robust theoretical framework for biomolecular simulations.

Main Methods:

  • Derivation of the Maxwell stress tensor for nonlinear Poisson-Boltzmann systems.
  • Formulation of analytical electrostatic forces based on the derived tensor.
  • Comparison with existing literature formulations.

Main Results:

  • Successfully derived analytical electrostatic forces from the Maxwell stress tensor.
  • Demonstrated that the new formulations are applicable to nonlinear systems with singularities and discontinuous dielectrics.
  • Showcased improved applicability compared to traditional methods.

Conclusions:

  • The Maxwell stress tensor provides a powerful tool for deriving electrostatic forces in complex biomolecular systems.
  • This theoretical advancement facilitates better integration of continuum electrostatics with molecular mechanics simulations.
  • The findings support more accurate structural and functional analyses of biomolecules.