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Energy Associated With a Charge Distribution

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.

Determining Electric Field From Electric Potential

Determining Electric Field From Electric Potential

The electric field and electric potential are related to each other. If the electric field at various points in the region of interest is known, it can be used to calculate the electric potential difference between any two points. Similarly, if the electric potential is known for various points, then it is possible to calculate the electric field.
In general, regardless of whether the electric field is uniform, it points in the direction of decreasing potential because the force on a positive...

Divergence and Curl of Electric Field

Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as

Electric Field

Electric Field

Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by defining a new physical quantity called the electric field.
In the new picture, imagine that the first charge sets up an electric field independent of all other charges in the universe. When another charge comes in its vicinity, the second charge experiences an electric force depending on the electric field at that point. The source charge does not...

Electric Field of a Charged Disk

Electric Field of a Charged Disk

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...

Induced Electric Fields: Applications

Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...

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Updated: Jul 30, 2025

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Gradient Bundle Analysis of Electric Field Induced Changes in Electron Charge Density.

Logan Epperson¹, Megan Mascarenas¹, Amanda Morgenstern¹

¹Department of Chemistry and Biochemistry, University of Colorado at Colorado Springs, Colorado Springs, Colorado 80918, United States.

The Journal of Physical Chemistry. A

|May 18, 2023

Summary

Electric fields (EFs) alter molecular electron density, influencing chemical reactions. This study quantifies these subtle charge density changes using gradient bundle analysis, providing insights for experimental design.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Molecular Physics

Background:

Electric fields (EFs) are known to induce electron charge density rearrangements in molecules.
Previous studies focused on EF effects on reactivity, controlling reaction rates and selectivity.
A fundamental understanding of EF-induced electron density changes is crucial for experimental applications.

Purpose of the Study:

To investigate how electric fields rearrange molecular electron charge density.
To determine the impact of molecular rotation and bond length changes on bond energies under EF.
To quantify EF-induced electron density redistribution within atomic basins.

Main Methods:

Applied electric fields to 10 diatomic and linear triatomic molecules.
Utilized gradient bundle (GB) analysis, an extension of quantum theory of atoms in molecules.
Calculated GB-condensed EF-induced densities using conceptual density functional theory.

Main Results:

Quantified subtle electron charge density rearrangements induced by electric fields.
Determined the influence of molecular constraints (rotation, bond length) on EF effects.
Established relationships between EF-induced densities and molecular properties like bond strength, polarity, and frontier molecular orbitals (FMOs).

Conclusions:

Gradient bundle analysis effectively captures EF-induced electron density changes.
Understanding these changes is key to predicting and controlling molecular behavior in electric fields.
The findings offer a foundation for designing experiments that leverage electric fields in chemistry.