Conventional Formulation of The Maxwell Equations (SI Units)
The precise formulation of the Maxwell equation depends on the precise definition of the quantities involved. Conventions differ with the unit systems because various definitions (and dimensions) are changed by absorbing dimensionfull factors like the speed of light c. This makes constants come out differently. The equations in this section are given in the convention used with SI units. Other units commonly used are CGS-Gaussian units based on the cgs system, Lorentz–Heaviside units (used mainly in particle physics) and Planck units (used in theoretical physics). See below for the formulation with CGS-Gaussian units.
In the following equations, symbols in bold represent vector quantities, and symbols in italics represent scalar quantities. The definitions of terms used in the two tables of equations are given in another table immediately following. For a detailed description of the differences between the microscopic (total charge and current) and macroscopic (free charge and current) variants of Maxwell's equations, see below.
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Integral formulation Name "Microscopic" equations "Macroscopic" equations Gauss's law Gauss's law for magnetism Maxwell–Faraday equation
(Faraday's law of induction)Ampère's circuital law
(with Maxwell's correction)
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Differential formulation Name "Microscopic" equations "Macroscopic" equations Gauss's law Gauss's law for magnetism Maxwell–Faraday equation
(Faraday's law of induction)Ampère's circuital law
(with Maxwell's correction)
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