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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: 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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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: 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 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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Gaussian Schell-model arrays.

Zhangrong Mei, Daomu Zhao, Olga Korotkova

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    We present a new type of light source that creates optical lattices with tunable patterns. This controllable light generation has potential applications in optical trapping and manipulation.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics

    Background:

    • Schell-model sources are widely used in optical beam generation.
    • Controlling far-field intensity patterns is crucial for applications like optical trapping.

    Purpose of the Study:

    • To introduce a novel class of planar, quasi-homogeneous Schell-model source.
    • To derive beam conditions for generating optical lattice average intensity patterns.

    Main Methods:

    • Developing a new quasi-homogeneous Schell-model source.
    • Analyzing the correlation properties of the source field.
    • Deriving mathematical conditions for beam formation.

    Main Results:

    • The source produces far fields with optical lattice average intensity patterns.
    • Tunable control over array dimension, lobe intensity, and lattice periodicity is achieved by adjusting correlation parameters.
    • Flat-topped intensity patterns can be generated with specific source parameter choices.

    Conclusions:

    • A novel, controllable optical lattice generation method is introduced.
    • The developed source offers flexible control over far-field intensity distributions.
    • Potential for generating tailored optical fields for various applications.