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Related Concept Videos

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: 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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Symmetry in Maxwell's Equations01:28

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Gauss's Law01:07

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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 in Dielectrics01:17

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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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Related Experiment Video

Updated: Mar 9, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Asymmetric Gaussian optical vortex.

Victor V Kotlyar, Alexey A Kovalev, Alexey P Porfirev

    Optics Letters
    |January 7, 2017
    PubMed
    Summary

    This study explores asymmetric Gaussian optical vortex beams, revealing crescent shapes that rotate during propagation. The research derives a fractional orbital angular momentum for these beams, showing its dependence on beam properties.

    Area of Science:

    • Optics and Photonics
    • Laser Physics

    Background:

    • Gaussian optical beams are fundamental in laser physics.
    • Optical vortices carry orbital angular momentum (OAM).
    • Off-axis vortex embedding creates asymmetric beam structures.

    Purpose of the Study:

    • To theoretically investigate Gaussian optical beams with embedded off-axis optical vortices.
    • To experimentally generate and characterize these asymmetric beams.
    • To analyze the resulting beam shapes and orbital angular momentum.

    Main Methods:

    • Theoretical modeling of Gaussian beams with off-axis vortices.
    • Experimental generation using an off-axis spiral phase plate.
    • Analysis of beam propagation and orbital angular momentum.

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    Last Updated: Mar 9, 2026

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    Main Results:

    • Observed crescent beam shapes dependent on shift distance.
    • Demonstrated rotation of the crescent shape upon propagation.
    • Derived an analytical expression for fractional orbital angular momentum.
    • Showed OAM decreases with increasing shift and spirality.

    Conclusions:

    • Asymmetric Gaussian optical vortex beams exhibit unique propagation dynamics.
    • The orbital angular momentum is fractional and controllable.
    • Experimental findings qualitatively support theoretical predictions.