Maxwell's equations

Maxwell's equations are the set of four equations, attributed to James Clerk Maxwell (written by Oliver Heaviside), that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.

Maxwell's equations in terms of differential forms

In a vacuum, where ε and μ are constant everywhere, Maxwell's equations simplify considerably once you use the language of differential geometry and differential forms. Now, the electric and magnetic fields are jointly described by a 2-form in a 4-dimensional spacetime manifold which is usually called F. Maxwell's equations then reduce to

Related Topics:
Vacuum - Differential geometry - Differential form - Spacetime

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the Bianchi identity

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:dold{F}=0

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where d is the exterior derivative, and the source equation

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:d{*old{F}}=*old{J}

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where the * is the Hodge star. Here, the fields are represented in natural units where ε0 is 1. Here, J is a 1-form called the "electric current" satisfying the continuity equation

Related Topics:
Hodge star - Natural units - 1-form - Continuity equation

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:d{*old{J}}=0

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