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Related Concept Videos

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

Electric Field of a Continuous Line Charge

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...
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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Electric Field of a Charged Disk01:23

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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...
Calculations of Electric Potential II01:27

Calculations of Electric Potential II

An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

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Related Experiment Video

Updated: Jun 3, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

A closed form for the electrostatic interaction between two rod-like charged objects.

M Askari1, J Abouie

  • 1Physics Department, Shahrood University of Technology, Shahrood 36199-95161, Iran.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 26, 2011
PubMed
Summary
This summary is machine-generated.

We derived a formula for electrostatic interactions between charged rods. For rods of equal length, specific configurations show minimum energy, and their thermodynamic properties reveal a specific heat maximum at certain distances.

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Area of Science:

  • Computational Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Understanding electrostatic interactions is crucial in various scientific fields.
  • Charged rod-like objects are relevant models for molecules and materials.
  • Previous studies often simplified object shapes or orientations.

Purpose of the Study:

  • To calculate the electrostatic interaction energy between two arbitrarily oriented charged rods in 3D.
  • To investigate the thermodynamic properties of a one-dimensional system of such rods.

Main Methods:

  • Derivation of a closed-form analytical formula for electrostatic interaction energy.
  • Analysis of interaction energy minima for rods of equal length.
  • Introduction of scaled temperature to study thermodynamic properties, specifically specific heat.

Main Results:

  • A general formula for interaction energy based on separation, lengths, and orientations was obtained.
  • For equal-length rods and separations r ≤ 0.8l, two minimum energy configurations were identified.
  • The specific heat of a 1D system of charged rods exhibits a maximum at r < 0.8l.

Conclusions:

  • The derived formula provides a comprehensive tool for analyzing charged rod interactions.
  • The study reveals specific orientational preferences driven by electrostatic forces.
  • Thermodynamic behavior, particularly specific heat, is sensitive to inter-rod distance and temperature.