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Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, ... In the old SI system of units, ...
One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
The electric and magnetic fields E and B have the same dimensions in the Heaviside–Lorentz system, meaning it is easy to recall where factors of c go in the Maxwell equation. Every time derivative comes with a 1 / c, which makes it dimensionally the same as a space derivative. In contrast, in SI units [E] / [B] is [c].
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
SI units for Maxwell's equations and the particle physicist's sign convention for the signature of Minkowski space (+ − − −), will be used throughout this article. Relationship with the classical fields
The maxwell is a non-SI unit. [8] 1 maxwell = 1 gauss × 2. That is, one maxwell is the total flux across a surface of one square centimetre perpendicular to a magnetic field of strength one gauss. The weber is the related SI unit of magnetic flux, which was defined in 1946. [9] 1 maxwell ≘ 10 −4 tesla × (10 −2 metre) 2 = 10 −8 weber
The SI unit of the Poynting vector is the watt per square metre (W/m 2); kg/s 3 in SI base units. ... In the "microscopic" version of Maxwell's equations, ...
Maxwell introduced the term D, specific capacity of electric induction, in a form different from the modern and familiar notations. [3] It was Oliver Heaviside who reformulated the complicated Maxwell's equations to the modern form. It wasn't until 1884 that Heaviside, concurrently with Willard Gibbs and Heinrich Hertz, grouped the equations ...