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Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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 uniform...
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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

Gauss's Law: Cylindrical Symmetry

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,...
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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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Related Experiment Video

Updated: Jun 15, 2026

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Scattering in spherically symmetric media.

A Y Perelman

    Applied Optics
    |March 10, 2010
    PubMed
    Summary

    This study analyzes electromagnetic scattering in layered spherical media. Exact energy expressions were derived, and a modified Mie problem confirmed scattering and extinction cross-section coincidence for transparent shells.

    Area of Science:

    • Electromagnetic theory
    • Wave propagation
    • Scattering phenomena

    Background:

    • Investigates electromagnetic scattering in spherically symmetric, multilayered media.
    • Considers perturbation sources in the external region of the medium.

    Purpose of the Study:

    • To derive exact expressions for field energy characteristics.
    • To analyze scattering from a dielectric coated sphere with specific refractive index properties.
    • To introduce and utilize a generalized phase angle transformation.

    Main Methods:

    • Representation of electromagnetic field vectors using potentials suitable for azimuthal dependence.
    • Analysis of permittivity and conductivity relationship to electric charge density.
    • Application of a modified Mie problem approach.

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    Scattering And Absorption of Light in Planetary Regoliths
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  • Introduction of the generalized van de Hulst phase angle transformation.

    • Main Results:

    • Proved linear dependence between permittivity and conductivity is equivalent to vanishing electric charge density.
    • Derived exact expressions for field energy characteristics in the external region.
    • Demonstrated coincidence of scattering and extinction cross sections for transparent spherical shells.

    Conclusions:

    • The methods provide exact field energy characteristics without wave zone assumptions.
    • The study successfully models scattering from a dielectric sphere with discontinuous refractive index derivatives.
    • The generalized phase angle transformation offers insights into scattering and extinction properties.