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The density of the linear momentum of the electromagnetic field is S/c 2 where S is the magnitude of the Poynting vector and c is the speed of light in free space. The radiation pressure exerted by an electromagnetic wave on the surface of a target is given by P r a d = S c . {\displaystyle P_{\mathrm {rad} }={\frac {\langle S\rangle }{\mathrm ...
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
The Poynting vector = represents the direction and magnitude of the power flow in the electromagnetic field (the length of the vectors shown here are not to scale; only the direction is being shown) In the region of space around the battery, the Poynting vectors are directed outward, indicating that power flows out from the battery into the ...
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
The Poynting vector for a wave is a vector whose component in any direction is the irradiance (power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is 1 / 2 Re{ E × H ∗ } , where E and H are due only to the wave in question, and the asterisk denotes ...
So, dimensionally, the Poynting vector is S = power / area = rate of doing work / area = ΔF / Δt Δx / area , which is the speed of light, c = Δx / Δt, times pressure, ΔF / area.
German physicist Heinrich Hertz first demonstrated the existence of radio waves in 1887 using what we now know as a dipole antenna (with capacitative end-loading). On the other hand, Guglielmo Marconi empirically found that he could just ground the transmitter (or one side of a transmission line, if used) dispensing with one half of the antenna, thus realizing the vertical or monopole antenna.
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.