Image theory for a point charge inside a layered dielectric sphere

1994 ◽  
Vol 77 (5) ◽  
pp. 327-335 ◽  
Author(s):  
J. C. -E. Sten ◽  
R. Ilmoniemi
Keyword(s):  
Point Charge ◽  
Image Theory ◽  
Dielectric Sphere ◽  
Layered Dielectric

Electrostatic image theory for layered dielectric sphere

1992 ◽  
Vol 139 (2) ◽  
pp. 186 ◽  
Author(s):  
I.V. Lindell ◽  
M.E. Ermutlu ◽  
A.H. Sihvola
Keyword(s):  
Image Theory ◽  
Dielectric Sphere ◽  
Layered Dielectric

Comment on “Surface-charge distribution on a dielectric sphere due to an external point charge: examples of C60 and C240 fullerenes, Phys. Chem. Chem. Phys., 2013, 15, 20115”

2014 ◽  
Vol 16 (28) ◽  
pp. 14969-14970
Author(s):  
Henning Zettergren ◽  
Fredrik Lindén ◽  
Henrik Cederquist
Keyword(s):  
Dielectric Properties ◽  
Surface Charge ◽  
Charge Distribution ◽  
Point Charge ◽  
Chem Phys ◽  
Dielectric Sphere ◽  
External Point ◽  
Surface Charge Distribution ◽  
Phys Chem Chem Phys

We show that the relative surface charge distribution from classical electrostatics cannot be used to discriminate between different assumptions about the dielectric properties of fullerenes interacting with external charges.

Electrostatic image theory for the dielectric sphere

Radio Science ◽  
1992 ◽  
Vol 27 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Ismo V. Lindell
Keyword(s):  
Image Theory ◽  
Dielectric Sphere

Low-frequency image theory for the dielectric sphere

1994 ◽  
Vol 8 (3) ◽  
pp. 295-313 ◽  
Author(s):  
I.V. Lindell ◽  
J.C.-E. Sten ◽  
R.E. Kleinman
Keyword(s):  
Low Frequency ◽  
Image Theory ◽  
Dielectric Sphere

scholarly journals New relationships between spherical and spheroidal harmonics and applications

2021 ◽  
Author(s):  
◽  
Matt Majic
Keyword(s):  
Spherical Harmonics ◽  
Point Charge ◽  
Coordinate Systems ◽  
Prolate Spheroidal ◽  
Dielectric Sphere ◽  
New Class ◽  
Spheroidal Harmonics ◽  
Physical Problems ◽  
Finite Line ◽  
Spheroidal Geometry

<p>This thesis deals with solutions to Laplace's equation in 3D, finding new relationships between solutions, manipulating these to find new approaches to physical problems, and proposing a new class of solutions. We mainly consider spherical and prolate spheroidal geometry and their corresponding solutions - spherical and spheroidal solid harmonics. We first present new relationships between these, expressing for example spherical harmonics as a series of spheroidal harmonics. Similar relationships are known but we work with the spherical and spheroidal coordinate systems being offset from each other. We also propose a new class of solutions which we call logopoles which have many links with spherical and spheroidal harmonics, and are related to the potential created by simple finite line charge distributions. Through the logopoles we find another relationship between the spheroidal harmonics and the often discarded alternate spherical harmonics. Then we apply one of the new spherical-spheroidal harmonic relationships to problems involving a point charge/dipole outside a dielectric sphere. We find new solutions where the potential is expanded as a series of spheroidal harmonics instead of the standard spherical ones, and we show that the convergence is much faster. We also solve these problems with logopoles and the solutions converge even faster, although they are more complicated as they involve a combination of logopoles and spherical harmonics.</p>

scholarly journals New relationships between spherical and spheroidal harmonics and applications

2021 ◽  
Author(s):  
◽  
Matt Majic
Keyword(s):  
Spherical Harmonics ◽  
Point Charge ◽  
Coordinate Systems ◽  
Prolate Spheroidal ◽  
Dielectric Sphere ◽  
New Class ◽  
Spheroidal Harmonics ◽  
Physical Problems ◽  
Finite Line ◽  
Spheroidal Geometry

<p>This thesis deals with solutions to Laplace's equation in 3D, finding new relationships between solutions, manipulating these to find new approaches to physical problems, and proposing a new class of solutions. We mainly consider spherical and prolate spheroidal geometry and their corresponding solutions - spherical and spheroidal solid harmonics. We first present new relationships between these, expressing for example spherical harmonics as a series of spheroidal harmonics. Similar relationships are known but we work with the spherical and spheroidal coordinate systems being offset from each other. We also propose a new class of solutions which we call logopoles which have many links with spherical and spheroidal harmonics, and are related to the potential created by simple finite line charge distributions. Through the logopoles we find another relationship between the spheroidal harmonics and the often discarded alternate spherical harmonics. Then we apply one of the new spherical-spheroidal harmonic relationships to problems involving a point charge/dipole outside a dielectric sphere. We find new solutions where the potential is expanded as a series of spheroidal harmonics instead of the standard spherical ones, and we show that the convergence is much faster. We also solve these problems with logopoles and the solutions converge even faster, although they are more complicated as they involve a combination of logopoles and spherical harmonics.</p>

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