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  2. Maxwell's equations - Wikipedia

    en.wikipedia.org/wiki/Maxwell's_equations

    The above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the (possibly atomic-level) charges and currents present. This is sometimes called the "general" form, but the macroscopic version below is equally general, the difference being one of bookkeeping.

  3. History of Maxwell's equations - Wikipedia

    en.wikipedia.org/wiki/History_of_Maxwell's_equations

    [24] [25] Maxwell deals with the motion-related aspect of electromagnetic induction, v × B, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, F = q ( E + v × B ) , which sits adjacent to Maxwell's equations and bears the name Lorentz force ...

  4. Maxwell relations - Wikipedia

    en.wikipedia.org/wiki/Maxwell_relations

    The structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem).

  5. A Dynamical Theory of the Electromagnetic Field - Wikipedia

    en.wikipedia.org/wiki/A_Dynamical_Theory_of_the...

    Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents (equation "A") with Ampère's circuital law (equation "C"). This amalgamation, which Maxwell himself had actually originally made at equation (112) in "On Physical Lines of Force", is the one that modifies Ampère's Circuital Law to include Maxwell's ...

  6. Classical electromagnetism - Wikipedia

    en.wikipedia.org/wiki/Classical_electromagnetism

    From Maxwell's equations, it is clear that ∇ × E is not always zero, and hence the scalar potential alone is insufficient to define the electric field exactly. As a result, one must add a correction factor, which is generally done by subtracting the time derivative of the A vector potential described below.

  7. Matrix representation of Maxwell's equations - Wikipedia

    en.wikipedia.org/wiki/Matrix_representation_of...

    One of the early uses of the matrix forms of the Maxwell's equations was to study certain symmetries, and the similarities with the Dirac equation. The matrix form of the Maxwell's equations is used as a candidate for the Photon Wavefunction. [8] Historically, the geometrical optics is based on the Fermat's principle of least time. Geometrical ...

  8. Covariant formulation of classical electromagnetism - Wikipedia

    en.wikipedia.org/wiki/Covariant_formulation_of...

    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.

  9. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    In fact, Maxwell's equations were crucial in the historical development of special relativity. However, in the usual formulation of Maxwell's equations, their consistency with special relativity is not obvious; it can only be proven by a laborious calculation. For example, consider a conductor moving in the field of a magnet. [8]