Maxwell's Equations, Maxwell's Equations

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The Lorentz force law itself was actually derived by Maxwell under the name of "Equation for Electromotive Force" and was one of an earlier set of eight Maxwell's equations.

Unlike the equations of mechanics (for example), Maxwell's equations are not unchanged in other unit systems. Though the general form remains the same, various definitions get changed and different constants appear at different places. Other than SI (used in engineering), the units commonly used are Gaussian units (based on the cgs system and considered to have some theoretical advantages over SI ), Lorentz-Heaviside units (used mainly in particle physics) and Planck units (used in theoretical physics).See below for CGS-Gaussian units.

It is only in this averaged sense that one can define quantities such as the permittivity and permeability of a material. At microscopic level, Maxwell's equations, ignoring quantum effects, describe fields, charges and currents in free space — but at this level of detail one must include all charges, even those at an atomic level, generally an intractable problem.

This extra equation appeared in an original list of eight Maxwell's equations in his 1865 paper entitled A Dynamical Theory of the Electromagnetic Field.

Plugging in these relations, it can be easily demonstrated that the two formulations of Maxwell's equations given in Section 1 are precisely equivalent.

These complications show there is merit in separating the Lorentz force from the main four Maxwell equations. The four Maxwell's equations express the fields' dependence upon current and charge, setting apart the calculation of these currents and charges. As noted in this subsection, these calculations may well involve the Lorentz force only implicitly. Separating these complicated considerations from the Maxwell's equations provides a useful framework.

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