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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

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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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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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

Gauss's Law: Planar Symmetry

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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...
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Gauss's Law01:07

Gauss's Law

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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.
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Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

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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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Quadratic Models01:23

Quadratic Models

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Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
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Updated: Dec 9, 2025

Author Spotlight: Unveiling the Potential of VSFG Microscopy in Studying Mesoscopically Heterogeneous Self-Assembled Structures
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Hollow rectangular multi-Gaussian Schell-model source.

Caifu Yuan, Simin Zheng, Xiaoling Ji

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |September 9, 2020
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed a novel hollow rectangular multi-Gaussian Schell-mode source. This new partially coherent source allows precise control over the far-zone spectral density distribution and hollow profile characteristics.

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    Area of Science:

    • Optics and Photonics
    • Wave Phenomena
    • Coherent Light Sources

    Background:

    • Partially coherent light sources are crucial in various optical applications.
    • Generating specific beam profiles, like hollow or ring shapes, presents unique challenges.
    • Controlling the spatial distribution of light intensity is essential for beam shaping.

    Purpose of the Study:

    • To introduce a new class of partially coherent source: the hollow rectangular multi-Gaussian Schell-mode source.
    • To analyze the relationship between source properties and far-zone spectral density.
    • To demonstrate control over the far-zone intensity profile characteristics.

    Main Methods:

    • Theoretical formulation of the hollow rectangular multi-Gaussian Schell-mode source.
    • Analysis of the spectral density distribution in the far-field.
    • Investigation of the influence of source structural parameters on the output beam.

    Main Results:

    • The proposed source generates a field with a hollow rectangular profile.
    • The far-zone spectral density distribution is dependent on the source's structural parameters.
    • Key profile characteristics, including hollow edge thickness, shape, size, and orientation, are controllable.

    Conclusions:

    • The hollow rectangular multi-Gaussian Schell-mode source offers a versatile method for generating tailored light fields.
    • Adjusting source parameters provides precise control over the far-zone intensity profile.
    • This development has potential applications in optical manipulation and imaging.