Maxwell’s Formulation – Differential Forms on Euclidean Space

Author: Jing Wang

Institute: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

One of the greatest advances in theoretical physics of the nineteenth century was Maxwell’s formulation of the the equations of electromagnetism. This article uses differential forms to solve a problem related to Maxwell’s formulation. The notion of differential form encompasses such ideas as elements of surface area and volume elements, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space or hyperspace. An important operation on differential forms is exterior differentiation, which generalizes the operators div, grad, curl of vector calculus. the study of differential forms, which was initiated by E.Cartan in the years around 1900, is often termed the exterior differential calculus.However, Maxwell’s equations have many very important implications in the life of a modern person, so much so that people use devices that function off the principles in Maxwell’s equations every day without even knowing it.

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