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Related Concept Videos

Gauss's Law01:07

Gauss's Law

8.3K
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.
8.3K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

7.6K
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...
7.6K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.3K
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,...
7.3K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.2K
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...
7.2K
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

2.6K
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...
2.6K
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

2.4K
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
2.4K

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Updated: May 4, 2026

Wastewater Irrigation Impacts on Soil Hydraulic Conductivity: Coupled Field Sampling and Laboratory Determination of Saturated Hydraulic Conductivity
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Hydraulic Conductivity Fields: Gaussian or Not?

Mark M Meerschaert1, Mine Dogan1, Remke L Van Dam1

  • 1Michigan State University, East Lansing, Michigan, USA.

Water Resources Research
|January 14, 2014
PubMed
Summary
This summary is machine-generated.

Statistical analysis of high-resolution hydraulic conductivity (K) data reveals that ground-penetrating radar (GPR) facies can reconcile Gaussian and non-Gaussian K field models. This finding impacts groundwater flow and transport simulations in alluvial aquifers.

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Area of Science:

  • Hydrogeology
  • Geophysics
  • Environmental Modeling

Background:

  • Hydraulic conductivity (K) fields are crucial for parameterizing groundwater flow and transport models.
  • Numerical simulations necessitate detailed K field representations, often synthesized from sparse data.
  • Recent high-resolution K (HRK) data and ground-penetrating radar (GPR) at the Macro Dispersion Experiment (MADE) site offer new insights.

Purpose of the Study:

  • To statistically analyze HRK and GPR data from the MADE site.
  • To investigate the implications for K field modeling in alluvial aquifers.
  • To address the controversy surrounding Gaussian versus non-Gaussian K field models.

Main Methods:

  • Statistical analysis of high-resolution hydraulic conductivity (HRK) data.
  • Application of a fractional difference filter to HRK data histograms.
  • Integration of ground-penetrating radar (GPR) facies for K field simulation.

Main Results:

  • A fractional difference filter organizes non-Gaussian ln K data into coherent distributions.
  • GPR facies enable the reproduction of non-Gaussian HRK data profiles using simulated Gaussian ln K fields within each facies.
  • The study reconciles differing observations of K field distributions at various scales.

Conclusions:

  • Both Gaussian and non-Gaussian K field models are valid, depending on the scale of observation.
  • GPR-derived facies provide a framework for integrating diverse K field characteristics.
  • This approach enhances the accuracy of groundwater flow and transport simulations in alluvial aquifers.