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Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation , these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays .
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation .
Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below. But the method of allocating a value to it is a consequence of the result that Maxwell's equations predict that, in free space, electromagnetic waves move with the speed of light.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In the old "electromagnetic (emu)" system of units, defined in the late 19th century, k m was chosen to be a pure number equal to 2, distance was measured in centimetres, force was measured in the cgs unit dyne, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current", the "abampere". A practical ...
To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern 'Heaviside' form of Maxwell's equations. Using (SI units) in a vacuum, these equations are ∇ ⋅ E = 0 {\displaystyle \nabla \cdot \mathbf {E} =0}
For the special case of an electromagnetic wave in a vacuum, in which the wave propagates at the speed of light, k is given by: = = where E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in a vacuum.
These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime. But because general relativity dictates that the presence of electromagnetic fields (or energy / matter in general) induce curvature in spacetime, [ 1 ] Maxwell's equations in flat ...