Related Experiment Video
Updated: Jun 4, 2026

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
Published on: October 16, 2017
Green's function of radial inhomogeneous spheres excited by internal sources
Grigorios P Zouros1, Gerassimos C Kokkorakis
1School of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece. zouros@mail.ntua.gr
Abstract:
Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.
Related Concept Videos
Electric Field of a Non Uniformly Charged Sphere
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: Spherical Symmetry
Calculations of Electric Potential I
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.
Gravitation Between Spherically Symmetric Masses
Gauss's Law: Cylindrical Symmetry
Spherical and Cylindrical Capacitor
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...

