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The equation PV = nRT represents the ideal gas law, where P is the pressure of the gas, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. Gibbs's free energy formula
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
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. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Download as PDF; Printable version; In other projects ... Equations Energy density in an EM wave ... The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons ...
Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile". Each propagates at generally different speeds determined by the important function called the dispersion relation .
The transmitted wave cannot, however, be a sinusoidal wave, since it would then transport energy away from the boundary, but since the incident and reflected waves have equal energy, this would violate conservation of energy. We therefore conclude that the transmitted wave must be a non-vanishing solution to Maxwell's equations that is not a ...
These equations say respectively: a photon has zero rest mass; the photon energy is hν = hc|k| (k is the wave vector, c is speed of light); its electromagnetic momentum is ħk [ħ = h/(2π)]; the polarization μ = ±1 is the eigenvalue of the z-component of the photon spin.
Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e., surface power density). The intensity of a wave is proportional to the square of its amplitude.