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Related Concept Videos

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

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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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Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

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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...
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Gauss's Law: Spherical Symmetry01:26

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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: 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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Beams01:30

Beams

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Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Circular Lorentz-Gauss beams.

Yiqing Xu, Guoquan Zhou

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |March 16, 2019
    PubMed
    Summary
    This summary is machine-generated.

    A new circular Lorentz-Gauss beam offers enhanced symmetry and is a valuable addition to existing optical beam types. This research details its properties and propagation through optical systems.

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    Area of Science:

    • Optics and Photonics
    • Beam Propagation Physics

    Background:

    • Lorentz-Gauss beams are widely used in optical systems.
    • Understanding beam propagation is crucial for optical system design.

    Purpose of the Study:

    • Introduce and analyze a novel circular Lorentz-Gauss beam.
    • Derive analytical expressions for its propagation through paraxial ABCD optical systems.
    • Compare its properties with the standard Lorentz-Gauss beam.

    Main Methods:

    • Derivation of the analytical optical field for the circular Lorentz-Gauss beam.
    • Utilizing second- and higher-order moments of light intensity.
    • Calculating beam propagation factor and kurtosis parameter.

    Main Results:

    • Analytical expressions for beam propagation factor and kurtosis parameter derived.
    • Demonstrated properties of circular Lorentz-Gauss beam in free space.
    • Circular Lorentz-Gauss beam exhibits superior symmetry compared to the standard Lorentz-Gauss beam.

    Conclusions:

    • The circular Lorentz-Gauss beam is an enrichment and supplement to existing Lorentz-Gauss beams.
    • Its enhanced symmetry and distinct properties make it suitable for advanced optical applications.
    • The derived analytical formulas facilitate its integration into optical system analysis.