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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.
Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm magnitude.
The...
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...

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Updated: Jun 16, 2026

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Light scattering by a spheroidal particle.

S Asano, G Yamamoto

    Applied Optics
    |February 6, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a method for solving electromagnetic scattering from prolate and oblate spheroidal particles of any size. The approach uses spheroidal wavefunctions and Maxwell

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    Area of Science:

    • Electromagnetic theory
    • Computational physics
    • Wave propagation

    Background:

    • Electromagnetic scattering from particles is crucial in various fields, including optics and remote sensing.
    • Analytical solutions for scattering by non-spherical particles are often complex.
    • Spheroidal particles are common in natural and artificial systems.

    Purpose of the Study:

    • To derive a general solution for electromagnetic scattering by homogeneous prolate and oblate spheroidal particles.
    • To provide a unified framework applicable to arbitrary particle sizes and refractive indices.
    • To analyze scattering under various incidence angles and polarization states.

    Main Methods:

    • Solving Maxwell's equations in spheroidal coordinates with appropriate boundary conditions.
    • Separating vector wave equations and expanding solutions in spheroidal wavefunctions.
    • Determining expansion coefficients by enforcing continuity of tangential electromagnetic field components.

    Main Results:

    • A unified solution form applicable to both prolate and oblate spheroids.
    • Formulation for oblique incidence involving transverse magnetic (TM) and transverse electric (TE) modes.
    • Results for axial incidence resemble the Mie theory solution for spheres.

    Conclusions:

    • The developed method provides a comprehensive analytical solution for electromagnetic scattering by spheroids.
    • The formulation offers flexibility for studying diverse scattering scenarios.
    • This work contributes to a deeper understanding of light-matter interactions with non-spherical particles.