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Related Concept Videos

Gauss's Law: Problem-Solving01:10

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 in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
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.
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,...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Gauss's Law: Spherical Symmetry01:26

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...

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Related Experiment Video

Updated: May 23, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Predicting cavity formation free energy: how far is the Gaussian approximation valid?

T Head-Gordon1, R M Lynden-Bell, John R Dowdle

  • 1Department of Bioengineering, University of California, Berkeley, California 94720, USA.

Physical Chemistry Chemical Physics : PCCP
|April 13, 2012
PubMed
Summary

The Gaussian model accurately describes water

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

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Last Updated: May 23, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

  • Physical Chemistry
  • Computational Chemistry
  • Soft Matter Physics

Background:

  • The Gaussian model is often used to describe density fluctuations in liquids.
  • Understanding these fluctuations is crucial for explaining the hydrophobic effect.
  • Deviations from Gaussian behavior can occur in various molecular fluids.

Purpose of the Study:

  • To assess the validity of the Gaussian model for water-like liquids.
  • To investigate the temperature dependence of the hydrophobic effect for small solutes.
  • To compare the behavior of different liquids with varying intermolecular potentials.

Main Methods:

  • Molecular dynamics simulations were performed.
  • The study analyzed liquids with intermolecular potentials differing from SPC/E water.
  • The focus was on small hard sphere solutes and their interactions.

Main Results:

  • Low compressibility liquids with close-packed structures deviate significantly from Gaussian fluctuations.
  • More compressible fluids with open networks show less deviation.
  • Water exhibits equilibrium density fluctuations well-described by Gaussian theory.

Conclusions:

  • Water's unique molecular structure allows for Gaussian fluctuations near solutes.
  • Minimal reorganization of solvent around solutes contributes to this.
  • This is linked to water's low solvent reorganization enthalpy and entropy.