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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.
Curvature of spacetime affects electrodynamics. An electromagnetic field having energy and momentum also generates curvature in spacetime. Maxwell's equations in curved spacetime can be obtained by replacing the derivatives in the equations in flat spacetime with covariant derivatives. (Whether this is the appropriate generalization requires ...
A Dynamical Theory of the Electromagnetic Field. " A Dynamical Theory of the Electromagnetic Field " is a paper by James Clerk Maxwell on electromagnetism, published in 1865. [1] In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment, and deduces that ...
t. e. 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.
t. e. Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant ...
The theory of special relativity plays an important role in the modern theory of classical electromagnetism. It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another. It sheds light on the relationship between ...
The third equation [C] relates the electromagnetic field to electromagnetic force. The rest of the equations [D] to [L] relates the electromagnetic field to material data: the current and charge densities as well as the material medium. Here the twelve Maxwell's equations have been given, respecting the original notations used by Maxwell.
However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations. [9] With the advent of special relativity, physical laws became amenable to the formalism of tensors. Maxwell's equations can be written in tensor form, generally ...