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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 uniform...

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Related Experiment Video

Updated: Jun 6, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

Local optical parameters of spherical polydispersions: simple approximations.

A A Kokhanovsky, E P Zege

|November 10, 2010

Summary

New analytical solutions accurately estimate optical properties of large spherical particles using geometric optics. Edge effects improve accuracy, showing good agreement with Mie theory for cloud applications.

Area of Science:

Optics and Photonics
Atmospheric Science

Background:

Accurate optical characteristics of polydispersions are crucial for atmospheric and material science.
Existing methods may lack efficiency or accuracy for large particles.

Purpose of the Study:

Derive new analytical solutions for local optical characteristics of spherical polydispersions.
Improve accuracy of geometric optics approximation for larger particles.

Main Methods:

Utilized the geometric optics (GO) approximation.
Incorporated edge effects to enhance GO accuracy.
Compared results with Mie theory calculations.

Main Results:

Developed novel analytical formulas for extinction and absorption coefficients.

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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

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Published on: August 13, 2019

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Derived formulas for asymmetry parameters of phase functions.

Demonstrated satisfactory accuracy compared to Mie theory.

Conclusions:

The new analytical solutions provide accurate estimations for optical properties of large spherical particles.
The derived formulas offer a simpler approach for calculating cloud optical characteristics.