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Related Concept Videos

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...
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: 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: 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,...
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
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...

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Related Experiment Video

Updated: Jun 20, 2026

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
06:49

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Radiation from anisotropic Gaussian Schell-model sources.

Y Li, E Wolf

    Optics Letters
    |August 28, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Researchers derived expressions for radiant intensity from anisotropic Gaussian Schell-model sources. With specific parameters, this intensity can achieve rotational symmetry, mimicking a coherent laser source.

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    Scattering And Absorption of Light in Planetary Regoliths
    11:34

    Scattering And Absorption of Light in Planetary Regoliths

    Published on: July 1, 2019

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    Last Updated: Jun 20, 2026

    In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
    06:49

    In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

    Published on: March 2, 2021

    Scattering And Absorption of Light in Planetary Regoliths
    11:34

    Scattering And Absorption of Light in Planetary Regoliths

    Published on: July 1, 2019

    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Mathematical Physics

    Background:

    • Gaussian Schell-model sources are widely used to model partially coherent light beams.
    • Understanding the radiant intensity distribution is crucial for applications in optical imaging and remote sensing.
    • Anisotropy and coherence state significantly influence the spatial distribution of light intensity.

    Purpose of the Study:

    • To derive general expressions for the radiant intensity of a planar, anisotropic, Gaussian, Schell-model source.
    • To investigate the conditions under which the radiant intensity exhibits rotational symmetry.
    • To compare the radiant intensity of such sources with that of coherent laser sources.

    Main Methods:

    • Mathematical derivation of radiant intensity using coherence theory.
    • Analysis of source parameters, including anisotropy and degree of coherence.
    • Comparison of derived expressions with established models for coherent and partially coherent sources.

    Main Results:

    • General expressions for radiant intensity were obtained for anisotropic Gaussian Schell-model sources.
    • It was demonstrated that specific source parameter choices can lead to rotationally symmetric radiant intensity.
    • The derived radiant intensity can be made identical to that of a rotationally symmetric, coherent laser source.

    Conclusions:

    • Planar, anisotropic Gaussian Schell-model sources offer versatile control over radiant intensity distributions.
    • Rotational symmetry in radiant intensity can be achieved by tuning source parameters, bridging the gap between partially coherent and coherent sources.
    • These findings have implications for designing and controlling light sources in various optical systems.