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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.
All but the last term of can be written as the tensor divergence of the Maxwell stress tensor, giving: = +, As in the Poynting's theorem, the second term on the right side of the above equation can be interpreted as the time derivative of the EM field's momentum density, while the first term is the time derivative of the momentum density for ...
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
Maxwell's equations can also be written in a fully symmetric form if one allows for "magnetic charge" analogous to electric charge. [20] With the inclusion of a variable for the density of magnetic charge, say ρ m , there is also a " magnetic current density" variable in the equations, j m .
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