Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Coulomb's Law

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...

Coulomb's Law and The Principle of Superposition

Coulomb's Law and The Principle of Superposition

Coulomb's Law describes the force experienced by two point charges under each other's presence. But what if there are more than two charges? For example, if there is a third charge, does it experience a force that is a simple combination of the individual forces due to the first two charges? Can it be described mathematically?
The Principle of Superposition answers the question. Yes, Coulomb's Law applies to each pair of charges, and the net force on each charge is the vector sum of the...

Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...

Gauss's Law: Problem-Solving

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...

Gauss's Law: Spherical Symmetry

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

Differential Form of Maxwell's Equations

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.

You might also read

Related Articles

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

Sort by

Same author

Buckling of two-dimensional plasma crystals with nonreciprocal interactions.

Physical review. E·2020

Same author

Full melting of a two-dimensional complex plasma crystal triggered by localized pulsed laser heating.

Physical review. E·2018

Same author

Flame propagation in two-dimensional solids: Particle-resolved studies with complex plasmas.

Physical review. E·2018

Same author

Instabilities in bilayer complex plasmas: Wake-induced mode coupling.

Physical review. E·2017

Same author

Wave modes in shear-deformed two-dimensional plasma crystals.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015

Same author

Simple estimation of thermodynamic properties of Yukawa systems.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014

Search research articles

Related Experiment Video

Updated: May 13, 2026

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Coulomb expansion: analytical solutions.

¹Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse, 85741 Garching, Germany. ivlev@mpe.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 19, 2013

Summary

This summary is machine-generated.

Charged particle clouds expand uniformly in dilute plasma, with density decreasing over time. Velocity increases linearly toward the boundary, a phenomenon observed across all dimensions. In external fields, expansion becomes exponential.

More Related Videos

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

Related Experiment Videos

Last Updated: May 13, 2026

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

Area of Science:

Plasma Physics
Computational Physics

Background:

Charged particle clouds expand due to interparticle repulsion.
Understanding expansion dynamics is crucial for plasma modeling.

Purpose of the Study:

To analytically describe the expansion of charged particle clouds in various dimensions.
To investigate the influence of external fields on cloud expansion.

Main Methods:

Exact and approximate analytical solutions were derived.
Analysis considered one, two, and three-dimensional symmetries (planar, axial, spherical).
The study focused on dilute plasma where screening is negligible.

Main Results:

Homogeneous density distribution and linearly increasing velocity towards the boundary were observed, irrespective of dimensionality.
Density evolution follows a universal t(-1) decay in the absence of external fields.
In inhomogeneous external fields, density decreases exponentially after an initial stage.

Conclusions:

The expansion dynamics of charged particle clouds exhibit universal behavior across dimensions.
External fields significantly alter the expansion from a power-law decay to an exponential one.