ॐ-Electromagnetism in Vacuum
Faculty Mentor
Maxim Durach
Location
Russell Union Ballroom
Type of Research
On-going
Session Format
Poster Presentation
College
College of Science & Mathematics
Department
BCP
Abstract
The main problem of electromagnetism is predicting the interaction between arbitrary charge distributions placed in arbitrary environments. Here we present a list for determining the interaction between sources, potentials, and fields using the ॐ potential method for different geometries, where ॐ potential underlies both the source distribution J and the potential distribution A. To solve for different symmetries we apply multiple methods, one of which involves solving for the Green’s Function for the higher order Helmholtz equation, who’s solution gives the ॐ potential for the respective source distribution. This method was applied to solve for spherical symmetry point source, cylindrical symmetry line source, and cartesian symmetry plane source. For spherical symmetry the solution is a spherical wave propagating through space without decay. Cylindrical solution involves the Hankel function of first order, a cylindrical wave. The solution to Cartesian symmetry involves a wave propagating in one dimension diverging at infinity, matching known solutions for potentials for planar symmetries. To solve for more complicated geometry such as a finite rod we can use properties of linearity to integrate ॐ over a region and approximate the solution in the far field. These methods help to further investigate the nature of propagating fields in macroscopic isotropy media, bypassing the issues that come with Green’s Functions for microscopic Electromagnetism.
Program Description
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Start Date
4-23-2026 10:00 AM
End Date
4-23-2026 12:00 PM
Recommended Citation
Iucker, Ian A. and Durach, Maxim, "ॐ-Electromagnetism in Vacuum" (2026). GS4 Student Scholars Symposium. 27.
https://digitalcommons.georgiasouthern.edu/research_symposium/2026/2026/27
ॐ-Electromagnetism in Vacuum
Russell Union Ballroom
The main problem of electromagnetism is predicting the interaction between arbitrary charge distributions placed in arbitrary environments. Here we present a list for determining the interaction between sources, potentials, and fields using the ॐ potential method for different geometries, where ॐ potential underlies both the source distribution J and the potential distribution A. To solve for different symmetries we apply multiple methods, one of which involves solving for the Green’s Function for the higher order Helmholtz equation, who’s solution gives the ॐ potential for the respective source distribution. This method was applied to solve for spherical symmetry point source, cylindrical symmetry line source, and cartesian symmetry plane source. For spherical symmetry the solution is a spherical wave propagating through space without decay. Cylindrical solution involves the Hankel function of first order, a cylindrical wave. The solution to Cartesian symmetry involves a wave propagating in one dimension diverging at infinity, matching known solutions for potentials for planar symmetries. To solve for more complicated geometry such as a finite rod we can use properties of linearity to integrate ॐ over a region and approximate the solution in the far field. These methods help to further investigate the nature of propagating fields in macroscopic isotropy media, bypassing the issues that come with Green’s Functions for microscopic Electromagnetism.
