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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 ...
Euler's problem also covers the case when the particle is acted upon by other inverse-square central forces, such as the electrostatic interaction described by Coulomb's law. The classical solutions of the Euler problem have been used to study chemical bonding , using a semiclassical approximation of the energy levels of a single electron ...
This dimming follows the inverse square law, which states that the brightness of an object decreases as 1 ⁄ r 2, where r is the distance between the observer and the object. Starlight also follows the inverse square law. Light rays leave the star in equal amounts in all directions. The light rays create a sphere of light surrounding the star.
Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
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 ...
Therefore, calculation of the total change in intensity involves both the inverse-square law and an estimation of attenuation over the path. The primary causes of attenuation in matter are the photoelectric effect , Compton scattering , and, for photon energies of above 1.022 MeV, pair production .
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space. One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.
The apparent magnitude is a measure of the diminishing flux of light as a result of distance according to the inverse-square law. [17] The Pogson logarithmic scale is used to measure both apparent and absolute magnitudes, the latter corresponding to the brightness of a star or other celestial body as seen if it would be located at an ...