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The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is proportional to the strength of the local sources, and hence zero outside sources. Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, light, sound, and radiation ...
In addition, Newton had formulated, in Propositions 43–45 of Book 1 [16] and associated sections of Book 3, a sensitive test of the accuracy of the inverse square law, in which he showed that only where the law of force is calculated as the inverse square of the distance will the directions of orientation of the planets' orbital ellipses stay ...
The lack of reflections in a free field means that any sound in the field is entirely determined by a listener or microphone because it is received through the direct sound of the sound source. This makes the open field a direct sound field. [3] In a free field, sound is attenuated with increased distance according to the inverse-square law. [1]
Radio propagation is the behavior of radio waves as they travel, or are propagated, from one point to another in vacuum, or into various parts of the atmosphere. [1]: 26‑1 As a form of electromagnetic radiation, like light waves, radio waves are affected by the phenomena of reflection, refraction, diffraction, absorption, polarization, and scattering. [2]
By contrast, the near-field ' s E and B strengths decrease more rapidly with distance: The radiative field decreases by the inverse-distance squared, the reactive field by an inverse-cube law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power ...
Because such radiation expands as it passes through space, and as its energy is conserved (in vacuum), the intensity of all types of radiation from a point source follows an inverse-square law in relation to the distance from its source. Like any ideal law, the inverse-square law approximates a measured radiation intensity to the extent that ...
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law [1] of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force . [ 2 ]
Finding the shape of the orbits that an inverse-square force law will produce is known as the Kepler problem. The Kepler problem can be solved in multiple ways, including by demonstrating that the Laplace–Runge–Lenz vector is constant, [ 51 ] or by applying a duality transformation to a 2-dimensional harmonic oscillator. [ 52 ]