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

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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: Planar Symmetry01:27

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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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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.
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Related Experiment Video

Updated: May 1, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Evolution of conically diffracted Gaussian beams in free space.

Stephen D Grant, Amin Abdolvand

    Optics Express
    |March 26, 2014
    PubMed
    Summary

    We studied how conically diffracted beams evolve in free space after passing through biaxial crystals. Our findings show good agreement between experimental observations and theoretical models for beam evolution.

    Area of Science:

    • Optics and Photonics
    • Crystallography
    • Laser Physics

    Background:

    • Biaxial crystals, specifically monoclinic double tungstates like KGd(WO4)2, exhibit unique optical properties.
    • Conically diffracted beams display complex propagation dynamics influenced by crystal properties.
    • Understanding beam evolution is crucial for applications in laser technology and optical systems.

    Purpose of the Study:

    • To investigate the free space evolution of conically diffracted beams.
    • To analyze beam behavior in single and cascade crystal systems.
    • To compare experimental results with a theoretical model.

    Main Methods:

    • Utilizing four biaxial crystals of the monoclinic double tungstate family [Potassium Gadolinium Tungstate - KGd(WO4)2].

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  • Measuring longitudinal shifts and radii of Hamilton-Lloyd rings.
  • Monitoring and quantifying the symmetric (forward and backward) evolution of the beam from its focal image plane.

    • Main Results:

    • Observed and quantified the free space evolution of conically diffracted beams.
    • Measured longitudinal shifts and radii of the Hamilton-Lloyd pair of rings.
    • Demonstrated good agreement between experimental patterns and theoretical predictions.

    Conclusions:

    • The study successfully characterized the free space evolution of conically diffracted beams through biaxial crystals.
    • Experimental data aligns well with the presented theoretical model, validating its predictive power.
    • Findings contribute to the understanding of light propagation in anisotropic optical media.