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Part of a series of articles about. Electromagnetism. Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.What is a quaternionic formulation of Maxwell's equations?
Historically, a quaternionic formulation was used. Maxwell's equations are partial differential equations that relate the electric and magnetic fields to each other and to the electric charges and currents.What is Maxwell’s third equation for the static magnetic field?
Extended Maxwell’s third equation or Maxwell’s third equation for the static magnetic field Which states that Static electric field vector is an irrotational vector. Static field implies the time-varying magnetic field is zero, ⇒ −δ→B δt =0 ⇒ − δ B → δ t = 0 ⇒ ▽× →E =0 ⇒ ▽ × E → = 0Are Maxwell's equations always covariant?
The resulting equations are clearly covariant (i.e. they look the same after you apply a Lorentz transformation), and look a lot simpler than Maxwell's equations in vector notation. This is one of my favorite examples of how differential forms can make life easier.