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Gauss's Law: Spherical Symmetry

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...

Symmetry in Maxwell's Equations

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...

Moments of Inertia for Composite Areas

Moments of Inertia for Composite Areas

Composite areas are structures with multiple basic shapes connected in some way. These shapes usually include rectangles, triangles, circles, and other basic shapes that are connected in such a way as to form a single structure. Calculating the second moment of area for a composite area is essential when trying to understand the structure's overall stiffness.
The second moment of area, also known as the moment of inertia, measures a structure's resistance to bending. It is calculated by...

Gauss's Law: Planar Symmetry

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...

Spherical Coordinates

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

Gauss's Law: Cylindrical Symmetry

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,...

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Related Experiment Video

Updated: Jun 9, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Hemispherical factors of model random-scattering composite materials.

L Servant, F Carmona

|September 8, 2010

Summary

This study investigates light scattering in germanium-particle-filled potassium bromide composites. A simple two-stream model accurately explains optical properties across various wavelengths and concentrations.

Area of Science:

Optical physics
Materials science
Condensed matter physics

Background:

Random composite materials exhibit complex light interaction phenomena.
Understanding light scattering is crucial for applications in optics and photonics.

Purpose of the Study:

To optically characterize 3D random composite materials.
To investigate the influence of germanium particle concentration and wavelength on optical properties.
To validate a simplified radiative transfer model for these composites.

Main Methods:

Optical experimental study in the visible and near-infrared spectrum (0.3–1.8 µm).
Measurement of hemispherical transmittance and reflectance.
Analysis using single scatterer properties and radiative transfer theory.

More Related Videos

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Published on: May 20, 2013

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Related Experiment Videos

Last Updated: Jun 9, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Published on: May 20, 2013

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Main Results:

Hemispherical transmittance and reflectance were measured for various composite concentrations.
A high asymmetry factor for germanium particle scattering was observed.
A simple two-stream theory effectively modeled the scattering behavior without adjustable parameters.

Conclusions:

The two-stream theory adequately interprets the main optical results.
The model's accuracy is demonstrated across different wavelengths and material compositions.
This provides a simplified yet effective approach for analyzing light scattering in such composites.