Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.2K
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.
4.2K
Electric Field of a Continuous Line Charge01:19

Electric Field of a Continuous Line Charge

2.4K
In physics, symmetry in a system means that something in the considered system remains unchanged due to a specific operation to which it is subjected. For example, consider a horizontal square. The square looks the same if its right and left sides are interchanged. Hence, it is symmetric under a right-left interchange.
In calculations of electric fields, symmetry is of great use. For example, while calculating electric fields of continuous charge distributions.
Consider a line element with a...
2.4K
Electric Field of Two Equal and Opposite Charges01:30

Electric Field of Two Equal and Opposite Charges

7.0K
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.
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...
7.0K
Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

3.1K
The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
3.1K
Magnetic Field due to Moving Charges01:23

Magnetic Field due to Moving Charges

11.6K
A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
11.6K
Basic Equation for Pressure Field01:13

Basic Equation for Pressure Field

578
The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...
578

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Pharmacological manipulation of Ezh2 with salvianolic acid B results in tumor vascular normalization and synergizes with cisplatin and T cell-mediated immunotherapy.

Pharmacological research·2022
Same author

Laparoscopic Treatment Strategies for Liver Echinococcosis.

Infectious diseases and therapy·2022
Same author

Furosemide prevents membrane KCC2 downregulation during convulsant stimulation in the hippocampus.

IBRO neuroscience reports·2022
Same author

Effect of Normobaric Oxygen Inhalation Intervention on Microcirculatory Blood Flow and Fatigue Elimination of College Students After Exercise.

Frontiers in genetics·2022
Same author

Chemical analysis of Chrysosplenium from different species by UPLC-Q exactive orbitrap HRMS and HPLC-DAD.

Journal of pharmaceutical and biomedical analysis·2022
Same author

Correction to Inverting the Handedness of Circularly Polarized Luminescence from Light-Emitting Polymers Using Film Thickness.

ACS nano·2022

Related Experiment Video

Updated: Jan 23, 2026

In Vitro Multiparametric Cellular Analysis by Micro Organic Charge-modulated Field-effect Transistor Arrays
10:05

In Vitro Multiparametric Cellular Analysis by Micro Organic Charge-modulated Field-effect Transistor Arrays

Published on: September 20, 2021

2.8K

Poisson-Boltzmann equation with a random field for charged fluids.

Li Wan1, Ning-Hua Tong2

  • 1Department of Physics, Wenzhou University, Wenzhou 325035, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 8, 2019
PubMed
Summary

We introduce a modified Poisson-Boltzmann equation with random fields (RFPBE) to account for ion fluctuations in charged fluids. This new model reveals how ion movement is influenced by both random fields and electrostatic forces.

More Related Videos

Safe Experimentation in Optical Levitation of Charged Droplets Using Remote Labs
09:09

Safe Experimentation in Optical Levitation of Charged Droplets Using Remote Labs

Published on: January 10, 2019

8.3K
Hydrogen Charging of Aluminum using Friction in Water
07:50

Hydrogen Charging of Aluminum using Friction in Water

Published on: January 28, 2020

6.5K

Related Experiment Videos

Last Updated: Jan 23, 2026

In Vitro Multiparametric Cellular Analysis by Micro Organic Charge-modulated Field-effect Transistor Arrays
10:05

In Vitro Multiparametric Cellular Analysis by Micro Organic Charge-modulated Field-effect Transistor Arrays

Published on: September 20, 2021

2.8K
Safe Experimentation in Optical Levitation of Charged Droplets Using Remote Labs
09:09

Safe Experimentation in Optical Levitation of Charged Droplets Using Remote Labs

Published on: January 10, 2019

8.3K
Hydrogen Charging of Aluminum using Friction in Water
07:50

Hydrogen Charging of Aluminum using Friction in Water

Published on: January 28, 2020

6.5K

Area of Science:

  • Physical Chemistry
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • The classical Poisson-Boltzmann equation (CPBE) is a mean-field theory for ion distributions in charged fluids, averaging out ion fluctuations.
  • Understanding ion distribution is crucial in various fields, including electrochemistry and biophysics.

Purpose of the Study:

  • To develop a modified Poisson-Boltzmann equation that incorporates ion fluctuations.
  • To investigate the impact of ion fluctuations on ion distribution in charged fluids.
  • To provide a computationally feasible method for solving the modified equation.

Main Methods:

  • Derivation of a Random Field Poisson-Boltzmann Equation (RFPBE) using field theory.
  • Incorporation of ion fluctuation effects via multiplicative noise.
  • Development of a Monte Carlo method based on path integral representation for solving the RFPBE.
  • Application to a two-dimensional system to demonstrate the method's efficacy.

Main Results:

  • The RFPBE captures ion fluctuation effects, yielding different ion distributions than the CPBE.
  • Ion fluctuations enhance ion diffusion into the domain, promoting uniform distribution.
  • The final ion distribution results from a balance between ion fluctuation and electrostatic boundary forces.
  • The Monte Carlo method makes the RFPBE applicable to high-dimensional systems.

Conclusions:

  • The RFPBE offers a more comprehensive model for ion distributions in charged fluids by including ion fluctuations.
  • The study highlights the significant role of ion fluctuations in determining ion behavior.
  • The proposed Monte Carlo method provides a powerful tool for analyzing complex systems with ion fluctuations.