Inverse-square law

This diagram shows how the law works. The lines represent the flux emanating from the source. In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks The total number of flux lines depends on the strength of the source and is constant with increasing distance. A greater density of flux lines (lines per unit area) means a stronger field. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus the strength of the field is inversely proportional to the square of the distance from the source.

In physics, an inverse-square law is any physical law stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i Quantity is a kind of property which exists as magnitude or multitude Inverse --> Inverse is the opposite of something This word and its derivatives are used greatly This article is about proportionality the mathematical relation In Algebra, the square of a number is that number multiplied by itself Distance is a numerical description of how far apart objects are

1 Areas of application
2 Examples
- 2.1 Electromagnetic radiation
- 2.2 Acoustics
3 Field theory interpretation
4 See also
5 External links
6 Notes

Areas of application

In particular the inverse-square law applies in the following cases: doubling the distance between the light and the subject results in one quarter of the light hitting the subject.

Gravitation

Gravitation refers to the attraction between two objects with mass. Gravitation is a natural Phenomenon by which objects with Mass attract one another This law states:
The gravitation attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them.
If we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square. However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as point mass while calculating the gravitational force.
This law was first suggested by Ismael Bullialdus but put on a firm basis by Isaac Newton after Robert Hooke proposed the idea in a letter to Newton. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass Ismaël Bullialdus ( September 28, 1605 - November 25, 1694 (age 89 was a French Astronomer. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Robert Hooke, FRS (18 July 1635 – 3 March 1703 was an English Natural philosopher and Polymath who played an important role in the Hooke later accused Newton of plagiarism.

Electrostatics

The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb's law. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form The deviation of the exponent from 2 is less than one part in 10¹⁵. ^[1] This implies a limit on the photon rest mass. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena

Light and other electromagnetic radiation

The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source; so an object (of the same size) twice as far away, receives only ¼ the energy (in the same time period). In Physics, intensity is a measure of the time-averaged Energy Flux. In photometry, illuminance is the total Luminous flux incident on a surface per unit Area. Irradiance, radiant emittance, and radiant exitance are Radiometry terms for the power of Electromagnetic radiation at a surface per unit Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 A point source is a single identifiable localized source of something In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός

More generally, the irradiance, i. Irradiance, radiant emittance, and radiant exitance are Radiometry terms for the power of Electromagnetic radiation at a surface per unit e. , the intensity (or power per unit area in the direction of propagation), of a spherical wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by absorption or scattering). In Physics, intensity is a measure of the time-averaged Energy Flux. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for Wave propagation is any of the ways in which waves travel through a Waveguide. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe In Optics and Physics, a wavefront is the locus (a line, or in a Wave propagating in 3 dimensions a Surface) of In Physics, absorption of electromagnetic radiation is the process by which the Energy of a Photon is taken up by matter typically the electrons of an Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from

For example, the intensity of radiation from the Sun is 9140 watts per square meter at the distance of Mercury (0. The Sun (Sol is the Star at the center of the Solar System. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. 387AU); but only 1370 watts per square meter at the distance of Earth (1AU)—a threefold increase in distance results in a ninefold decrease in intensity of radiation. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001

Photographers and theatrical lighting professionals use the inverse-square law to determine optimal location of the light source for proper illumination of the subject. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700

The fractional reduction in electromagnetic fluence (Φ) for indirectly ionizing radiation with increasing distance from a point source can be calculated using the inverse-square law. Since emissions from a point source have radial directions, they intercept at a perpendicular incidence. The area of such a shell is 4πr² where r is the radial distance from the center.

The law is particularly important in diagnostic radiography and radiotherapy treatment planing, though this proportionality does not hold in practical situations unless source dimensions are much smaller than the distance r. For medical radiography see Radiology Radiography is the use of X-rays to view unseen or hard-to-image objects Radiation therapy (or radiotherapy) is the medical use of Ionizing radiation as part of Cancer treatment to control Malignant

Acoustics

The inverse-square law is used in acoustics in measuring the sound intensity at a given distance from the source. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids The sound intensity, I, (acoustic intensity is defined as the Sound power Pac per unit area A. ^[2]

Examples

Electromagnetic radiation

Let the total power radiated from a point source, e. g. , an omnidirectional isotropic antenna, be $P \$ . An isotropic radiator is a theoretical Point source of waves which exhibits the same magnitude or properties when measured in all directions At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius $r \$ is $A = 4 \pi r^2 \$ , then intensity $I \$ of radiation at distance $r \$ is

$I = \frac{P}{A} = \frac{P}{4 \pi r^2}. \,$

$I \propto \frac{1}{r^2} \,$

$\frac{I_1} {I_2 } = \frac{{r_2}^2}{{r_1}^2} \,$

$I_1 = I_{2} \cdot {r_{2}^2} \cdot \frac{1}{{r_1}^2} \,$

The energy or intensity decreases by a factor of ¼ as the distance $r$ is doubled, or measured in dB it would decrease by 6. In Physics, intensity is a measure of the time-averaged Energy Flux. The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to 02 dB. This is the fundamental reason why intensity of radiation, whether it is electromagnetic or acoustic radiation, follows the inverse-square behaviour, at least in the ideal 3 dimensional context (propagation in 2 dimensions would follow a just an inverse-proportional distance behaviour and propagation in one dimension, the plane wave, remains constant in amplitude even as distance from the source changes). In Physics, intensity is a measure of the time-averaged Energy Flux. Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids In the Physics of Wave propagation (especially Electromagnetic waves, a plane wave (also spelled planewave) is a constant-frequency wave whose

Acoustics

In acoustics, the sound pressure of a spherical wavefront radiating from a point source decreases by 50% as the distance $r$ is doubled, or measured in dB it decreases by 6. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe In Optics and Physics, a wavefront is the locus (a line, or in a Wave propagating in 3 dimensions a Surface) of The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to 02 dB. The behaviour is not inverse-square, but is inverse-proportional:

$p \propto \frac{1}{r} \,$

$\frac{p_1} {p_2 } = \frac{r_2}{r_1} \,$

$p_1 = p_2 \cdot r_2 \cdot \frac{1}{r_1} \,$

However the same is also true for the component of particle velocity $v \,$ that is in-phase to the instantaneous sound pressure $p \,$ . Particle velocity is the velocity v of a particle (real or imagined in a medium as it transmits a Wave.

$v \propto \frac{1}{r} \,$

Only in the near field the quadrature component of the particle velocity is 90° out of phase with the sound pressure and thus does not contribute to the time-averaged energy or the intensity of the sound. The near field and far field of an antenna or other isolated source of Electromagnetic radiation are regions around the source where different parts of the field This quadrature component happens to be inverse-square. The sound intensity is the product of the RMS sound pressure and the RMS particle velocity (the in-phase component), both which are inverse-proportional, so the intensity follows an inverse-square behaviour as is also indicated above:

$I = p \cdot v \propto \frac{1}{r^2}. \,$

The inverse-square law pertained to sound intensity. The sound intensity, I, (acoustic intensity is defined as the Sound power Pac per unit area A. In Mathematics, the root mean square (abbreviated RMS or rms) also known as the quadratic mean, is a statistical measure of the Because sound pressures are more accessible to us, the same law can be called the "inverse-distance law".

Field theory interpretation

For an irrotational vector field in three-dimensional space the law corresponds to the property that the divergence is zero outside the source. In Vector calculus a conservative vector field is a Vector field which is the Gradient of a Scalar potential. In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the Generally, for irrotational vector field in n-dimensional Euclidean space, inverse (n − 1)^th potention law corresponds to the property of zero divergence outside the source.

External links

Notes

^ Williams, Faller, Hill (1971), “New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass”, Physical Review Letters 26: 721-724, <http://prola.aps.org/abstract/PRL/v26/i12/p721_1>
^ Inverse-Square law for sound

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain. In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. Physical Review Letters is one of the most prestigious journals in Physics. Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration A work of the United States government, as defined by United States copyright law, is "a work prepared by an officer or employee of the U The public domain is a range of abstract materials &ndash commonly referred to as Intellectual property &ndash which are not owned or controlled by anyone

Dictionary

-noun

(physics) any physical law, such as that of gravitation, in which a quantity varies inversely with distance from a source as the square of that distance

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Contents

Areas of application

Gravitation

Electrostatics

Light and other electromagnetic radiation

Acoustics

Examples

Electromagnetic radiation

Acoustics

Field theory interpretation

See also

External links

Notes

Dictionary

inverse-square law

-noun