Maxwell's Equations in Arbitrary Coordinate System

TL;DR

This paper uses tensorial formalism to derive Maxwell's equations in various coordinate systems, providing a unified approach that includes covariant and coordinate-specific forms, verified in cylindrical and spherical coordinates.

Contribution

It introduces a tensorial approach to Maxwell's equations applicable in arbitrary holonomic coordinate systems, bridging vector and tensor formalisms.

Findings

Derived Maxwell's equations in covariant and coordinate forms

Established relations between vector and tensor formalisms

Validated results in cylindrical and spherical coordinates

Abstract

The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the relation between vectorial and tensorial formalisms and differential operators for arbitrary holonomic coordinate system in coordinate form is given. The results obtained by tensorial and vectorial formalisms are verified in cylindrical and spherical coordinate systems.