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Wassp Mensen  !! I am  AZZIE SOSA. Ik woon in   Atlanta  . Ik draaien  40. I en mijn zus naar  The Giant Militaire School van Kind Onderwijs<br><br>Here is my web page :: [http://oilandgasstaffunion.com/people/lasawyers spiderman]
{{Electromagnetism|cTopic=Electrostatics}}
 
'''Coulomb's law''', or Coulomb's [[inverse-square law]], is a [[physical law|law]] of [[physics]] describing the [[electrostatic]] interaction between [[electric charge|electrically charged]] particles. The law was first published in 1785 by French physicist [[Charles-Augustin de Coulomb|Charles Augustin de Coulomb]] and was essential to the development of the [[classical electromagnetism|theory of electromagnetism]]. It is analogous to [[Isaac Newton]]'s inverse-square [[Newton's law of universal gravitation|law of universal gravitation]]. Coulomb's law can be used to derive [[Gauss's law]], and vice versa. The law has been [[tests of electromagnetism|tested heavily]], and all observations have upheld the law's principle.
 
== History ==
<!--Please grow the size in px for these two side images as the history section grows-->
[[File:Coulomb.jpg|thumb|left|Charles Augustin de Coulomb]]
 
Ancient cultures around the [[Mediterranean Sea|Mediterranean]] knew that certain objects, such as rods of [[amber]], could be rubbed with cat's fur to attract light objects like feathers. [[Thales of Miletus]] made a series of observations on [[static electricity]] around 600 BC, from which he believed that [[friction]] rendered amber [[magnetic]], in contrast to minerals such as [[magnetite]], which needed no rubbing.<ref name=stewart>
{{Cite book
| first = Joseph | last= Stewart
| title = Intermediate Electromagnetic Theory
| publisher = World Scientific
| year = 2001
| page = 50
| isbn = 981-02-4471-1
| postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}
</ref><ref>
{{Cite book
| first = Brian | last = Simpson
| title = Electrical Stimulation and the Relief of Pain
| publisher = Elsevier Health Sciences
| year = 2003
| pages = 6–7
| isbn =0-444-51258-6
| postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}
</ref> Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between [[magnetism]] and [[electricity]]. Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist [[William Gilbert (astronomer)|William Gilbert]] made a careful study of electricity and magnetism, distinguishing the [[lodestone]] effect from [[static electricity]] produced by rubbing amber.<ref name=stewart/> He coined the [[New Latin]] word ''electricus'' ("of amber" or "like amber", from ''ήλεκτρον'' [''elektron''], the Greek word for "amber") to refer to the property of attracting small objects after being rubbed.<ref>
{{Cite book
| first = Brian | last = Baigrie
| title = Electricity and Magnetism: A Historical Perspective
| publisher = Greenwood Press
| year = 2006
| pages = 7–8
| isbn = 0-313-33358-0
| postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}
</ref> This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in [[Thomas Browne]]'s ''[[Pseudodoxia Epidemica]]'' of 1646.<ref>
{{Cite journal
| first = Gordon | last = Chalmers
| title = The Lodestone and the Understanding of Matter in Seventeenth Century England
| journal = Philosophy of Science
| year = 1937
| volume = 4
| issue = 1
| pages = 75–95
| doi = 10.1086/286445
| postscript = <!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}</ref>
 
Early investigators of the 18th century who suspected that the electrical force diminished with distance as the [[force]] of [[gravity]] did (i.e., as the inverse square of the distance) included [[Daniel Bernoulli]]<ref>
{{cite book
|last=Socin
|first=Abel
|title=Acta Helvetica Physico-Mathematico-Anatomico-Botanico-Medica
|url=http://www.archive.org/stream/actahelveticaphy04helv#page/224/mode/2up
|volume=4
|year=1760
|publisher=Basileae
|language=Latin
|pages=224, 225}}</ref> and [[Alessandro Volta]], both of whom measured the force between plates of a [[capacitor]], and [[Franz Aepinus]] who supposed the inverse-square law in 1758.<ref>
{{cite book
|last=Heilbron
|first=J.L.
|authorlink=John L. Heilbron
|title=Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics
|url=http://books.google.es/books?id=UlTLRUn1sy8C
|isbn=0486406881
|location=Los Angeles, California
|year=1979
|publisher=University of California Press
|pages=[http://books.google.es/books?id=UlTLRUn1sy8C&pg=PA460#v=onepage&q&f=false 460–462] and [http://books.google.com/books?id=UlTLRUn1sy8C&pg=PA464#v=onepage&q&f=false 464] (including footnote 44)}}</ref>
 
Based on experiments with [[electrically charged]] spheres, [[Joseph Priestley]] of England was among the first to propose that electrical force followed an [[inverse-square law]], similar to [[Newton's law of universal gravitation]]. However, he did not generalize or elaborate on this.<ref>
{{cite book
|last=Schofield
|first=Robert E.
|title=The Enlightenment of Joseph Priestley: A Study of his Life and Work from 1733 to 1773
|year=1997
|publisher=University Park: Pennsylvania State University Press
|pages=144–56
|isbn=0-271-01662-0}}</ref> In 1767, he conjectured that the force between charges varied as the inverse square of the distance.<ref>
{{cite book
|last=Priestley
|first=Joseph
|title=The History and Present State of Electricity, with Original Experiments
|url=http://archive.org/stream/historyandprese00priegoog#page/n6/mode/2up
|year=1767
|location=London, England
|page=732}}<br /><blockquote>May we not infer from this experiment, that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated, that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?</blockquote></ref><ref>
{{Cite book
|first = Robert S.
|last = Elliott
| title = Electromagnetics: History, Theory, and Applications
| url = http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0780353846.html
| year = 1999
| isbn = 978-0-7803-5384-8
| postscript = <!--None-->}}</ref>
 
[[Image:Bcoulomb.png|thumb|Coulomb’s [[torsion balance]]]]
 
In 1769, Scottish physicist [[John Robison (physicist)|John Robison]] announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x<sup>-2.06</sup>.<ref>
{{cite book
|last = Robison
|first = John
|editor-first = John
|editor-last = Murray
|title = A System of Mechanical Philosophy
|url = http://archive.org/stream/asystemmechanic07wattgoog#page/n5/mode/2up
|volume = 4
|year = 1822
|location = London, England }}<br />On [http://books.google.es/books?id=8pRDAAAAcAAJ&pg=PA68&redir_esc=y#v=onepage&q&f=false page 68], the author states that in 1769 he announced his findings regarding the force between spheres of like charge. On [http://books.google.com/books?id=8pRDAAAAcAAJ&pg=PA73#v=onepage&q&f=false page 73], the author states the force between spheres of like charge varies as x<sup>-2.06</sup>:<br /><blockquote>The result of the whole was, that the mutual repulsion of two spheres, electrified positively or negatively, was very nearly in the inverse proportion of the squares of the distances of their centres, or rather in a proportion somewhat greater, approaching to x<sup>-2.06</sup>.</blockquote>When making experiments with charged spheres of opposite charge the results were similar, as stated on [http://books.google.com/books?id=8pRDAAAAcAAJ&pg=PA73#v=onepage&q&f=false page 73]:<br /><blockquote>When the experiments were repeated with balls having opposite electricities, and which therefore attracted each other, the results were not altogether so regular and a few irregularities amounted to 1/6 of the whole; but these anomalies were as often on one side of the medium as on the other. This series of experiments gave a result which deviated as little as the former (or rather less) from the inverse duplicate ratio of the distances; but the deviation was in defect as the other was in excess.</blockquote>Nonetheless, on [http://books.google.com/books?id=8pRDAAAAcAAJ&pg=PA74#v=onepage&q&f=false page 74] the author infers that the actual action is related exactly to the inverse duplicate of the distance:<br><blockquote>We therefore think that it may be concluded, that the action between two spheres is exactly in the inverse duplicate ratio of the distance of their centres, and that this difference between the observed attractions and repulsions is owing to some unperceived cause in the form of the experiment.</blockquote>On [http://books.google.com/books?id=8pRDAAAAcAAJ&pg=PA75#v=onepage&q&f=false page 75], the authour compares the electric and gravitational forces:<br /><blockquote>Therefore we may conclude, that the law of electric attraction and repulsion is similar to that of gravitation, and that each of those forces diminishes in the same proportion that the square of the distance between the particles increases.</blockquote></ref>
 
In the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by [[Henry Cavendish]] of England.<ref>{{cite book |editor-last=Maxwell |editor-first=James Clerk |title=The Electrical Researches of the Honourable Henry Cavendish... |url=http://www.archive.org/stream/electricalresear00caveuoft |edition=1st |origyear=1879 |year=1967 |publisher=Cambridge University Press |location=Cambridge, England |pages=104–113 |chapter=Experiments on Electricity: Experimental determination of the law of electric force. |chapterurl=http://www.archive.org/stream/electricalresear00caveuoft#page/104/mode/2up}}<br />On [http://www.archive.org/stream/electricalresear00caveuoft#page/111/mode/2up pages 111 and 112] the author states:<blockquote>We may therefore conclude that the electric attraction and repulsion must be inversely as some power of the distance between that of the 2 + 1/50 th and that of the 2 - 1/50 th, and there is no reason to think that it differs at all from the inverse duplicate ratio.</blockquote></ref>
 
Finally, in 1785, the French physicist [[Charles-Augustin de Coulomb]] published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the [[classical electromagnetism|theory of electromagnetism]].<ref name="1785a"/> He used a [[torsion balance]] to study the repulsion and attraction forces of [[charged particle]]s, and determined that the magnitude of the electric force between two [[point charge]]s is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
 
The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak [[torsion spring]]. In Coulomb's experiment, the torsion balance was an [[Insulator (electricity)|insulating]] rod with a [[metal]]-coated ball attached to one end, suspended by a [[silk]] thread. The ball was charged with a known charge of [[static electricity]], and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the [[scientific instrument|instrument]]. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law.
 
== The law ==
 
Coulomb's law states that:
 
:''The magnitude of the electrostatic [[force]] of interaction between two point [[electric charge|charges]] is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them.''<ref name="1785a">In -- Coulomb (1785a) [http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA569#v=onepage&q&f=false "Premier mémoire sur l’électricité et le magnétisme,"] ''Histoire de l’Académie Royale des Sciences'', pages 569-577 -- Coulomb studied the repulsive force between bodies having electrical charges of the same sign: <br /><blockquote>''Page 574'' : Il résulte donc de ces trois essais, que l'action répulsive que les deux balles électrifées de la même nature d'électricité exercent l'une sur l'autre, suit la raison inverse du carré des distances.</blockquote><blockquote>''Translation'' : It follows therefore from these three tests, that the repulsive force that the two balls --[that were] electrified with the same kind of electricity -- exert on each other, follows the inverse proportion of the square of the distance.</blockquote>In -- Coulomb (1785b) [http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA578#v=onepage&q&f=false "Second mémoire sur l’électricité et le magnétisme,"] ''Histoire de l’Académie Royale des Sciences'', pages 578-611. -- Coulomb showed that oppositely charged bodies obey an inverse-square law of attraction.</ref>
:''The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.''
 
[[Image:Coulombslaw.svg|center|A graphical representation of Coulomb's law]]
 
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Coulomb's law can also be stated as a simple mathematical expression. The [[Scalar (mathematics)|scalar]] and [[Vector space|vector]] forms of the mathematical equation are
:<math>|\mathbf F|=k_e{|q_1q_2|\over r^2}\qquad</math> and <math>\qquad\mathbf F_1=k_e\frac{q_1q_2}{{|\mathbf r_{21}|}^2} \mathbf{\hat{r}}_{21},\qquad</math> respectively,
 
where <math>k_e</math> is [[Coulomb's constant]] (<math>k_e  = 8.987\,551\,787\,368\,176\,4\times 10^9\ \mathrm{N\cdot m^2\cdot C}^{-2}</math>), <math>q_1</math> and <math>q_2</math> are the signed magnitudes of the charges, the scalar <math>r</math> is the distance between the charges, the vector <math>\boldsymbol{r_{21}}=\boldsymbol{r_1-r_2}</math> is the vectorial distance between the charges, and <math>\boldsymbol{\hat{r}_{21}}={\boldsymbol{r_{21}}/|\boldsymbol{r_{21}}|}</math> (a unit vector pointing from <math>q_2</math> to <math>q_1</math>). The vector form of the equation calculates the force <math>\mathbf F_1</math> applied on <math>q_1</math> by <math>q_2</math>. If <math>\mathbf r_{12}</math> is used instead, then the effect on <math>q_2</math> can be found. It can be also calculated using [[Newton's third law]]: <math>\mathbf F_2=-\mathbf F_1</math>.
 
=== Units ===
[[Electromagnetic theory]] is usually expressed using [[SI|the standard SI units]]. Force is measured in [[Newton (unit)|newtons]], charge in [[coulomb]]s, and distance in [[metre]]s. Coulomb's constant is given by <math>k_e = 1 / (4\pi\varepsilon_0\varepsilon)</math>. The constant <math>\varepsilon_0</math> is the [[permittivity]] of free space in C<sup>2</sup> m<sup>−2</sup> N<sup>−1</sup>. And <math>\varepsilon</math> is the [[relative permittivity]] of the material in which the charges are immersed, and is dimensionless.
 
The [[SI derived units]] for the electric field are [[volt]]s per meter, newtons per coulomb, or [[tesla (unit)|tesla]] meters per second.
 
Coulomb's law and [[Coulomb's constant]] can also be interpreted in various terms:
:* [[Atomic units]]. In atomic units the force is expressed in [[hartree]]s per [[Bohr radius]], the charge in terms of the [[elementary charge]], and the distances in terms of the ''Bohr radius''.
:* [[Electrostatic units]] or [[Gaussian units]]. In electrostatic units and Gaussian units, the unit charge (''esu'' or [[statcoulomb]]) is defined in such a way that the Coulomb constant {{math|''k''}} disappears because it has the value of one and becomes [[dimensionless]].
 
===Electric field===
[[File:Electric field one charge changing.gif|thumb|If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.]]
 
An electric field is a [[vector field]] that associates to each point in space the Coulomb force experienced by a [[Test_particle#Test_particles_in_plasma_physics_or_electrodynamics|test charge]]. In the simplest case, the field is considered to be generated solely by a single source [[point charge]]. The strength and direction of the Coulomb force <math>\boldsymbol{F}</math> on a test charge <math>q_t</math> depends on the electric field <math>\boldsymbol{E}</math> that it finds itself in, such that <math>\boldsymbol{F} = q_t \boldsymbol{E}</math>. If the field is generated by a positive source point charge <math>q</math>, the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge <math>q_t</math> would move if placed in the field. For a negative point source charge, the direction is radially inwards.
 
The magnitude of the electric field <math>\boldsymbol{E}</math> can be derived from [[Coulomb's_law#The_law|Coulomb's law]]. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the [[electric field]] <math>\boldsymbol{E}</math> created by a single source [[point charge]] <math>q</math> at a certain distance from it <math>r</math> in vacuum is given by:
 
:<math>|\boldsymbol{E}|={1\over4\pi\varepsilon_0}{|q|\over r^2}</math>.
 
===Coulomb's constant===
{{main|Coulomb's constant}}
 
Coulomb's constant is a proportionality factor that appears in Coulomb's law as well as in other electric-related formulas. Denoted <math>k_e</math>, it is also called the electric force constant or electrostatic constant, hence the subscript <math>e</math>.
 
The exact value of Coulomb's constant is:
:<math>\begin{align}
k_e &= \frac{1}{4\pi\varepsilon_0}=\frac{c_0^2\mu_0}{4\pi}=c_0^2\times 10^{-7}\ \mathrm{H\cdot m}^{-1}\\
&= 8.987\,551\,787\,368\,176\,4\times 10^9\ \mathrm{N\cdot m^2\cdot C}^{-2}
\end{align}</math>
 
===Conditions for validity===
There are two conditions to be fulfilled for the validity of Coulomb’s law:
#The charges considered must be point charges.
#They should be stationary with respect to each other.
 
==Scalar form==
[[Image:CoulombsLaw.svg|thumb|right|The absolute value of the force <math>\boldsymbol{F}</math> between two [[point charge]]s <math>q</math> and <math>Q</math> relates to the distance between the point charges and to the simple product of their charges. The diagram shows that like charges repel each other, and opposite charges attract each other.]]
 
When it is only of interest to know the magnitude of the electrostatic force (and not its direction), it may be easiest to consider a scalar version of the law. The [[scalar (mathematics)|scalar form]] of Coulomb's Law relates the magnitude and sign of the electrostatic force <math>\boldsymbol{F}</math> acting simultaneously on two point charges <math>q_1</math> and <math>q_2</math> as follows:
 
:<math>|\boldsymbol{F}|=k_e{|q_1q_2|\over r^2}</math>
 
where <math>r</math> is the separation distance and <math>k_e</math> is Coulomb's constant. If the product <math>q_1 q_2</math> is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c1 Coulomb's law], Hyperphysics</ref>
 
==Vector form==
[[Image:Coulombslaw.svg|thumb|right|350px|A graphical representation of Coulomb's law.|In the image, the vector <math>\boldsymbol{F}_1</math> is the force experienced by <math>q_1</math>, and the vector <math>\boldsymbol{F}_2</math> is the force experienced by <math>q_2</math>. When <math>q_1 q_2 > 0</math> the forces are repulsive (as in the image) and when <math>q_1 q_2 < 0</math> the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.]]
 
Coulomb's law states that the electrostatic force <math>\boldsymbol{F_1}</math> experienced by a charge, <math>q_1</math> at position <math>\boldsymbol{r_1}</math>, in the vicinity of another charge, <math>q_2</math> at position <math>\boldsymbol{r_2}</math>, in a vacuum is equal to:
 
:<math>\boldsymbol{F_1}={q_1q_2\over4\pi\varepsilon_0}{(\boldsymbol{r_1-r_2})\over|\boldsymbol{r_1-r_2}|^3}={q_1q_2\over4\pi\varepsilon_0}{\boldsymbol{\hat{r}_{21}}\over |\boldsymbol{r_{21}}|^2},</math>
 
where <math>\boldsymbol{r_{21}}=\boldsymbol{r_1-r_2}</math>, the unit vector <math>\boldsymbol{\hat{r}_{21}}={\boldsymbol{r_{21}}/|\boldsymbol{r_{21}}|}</math>, and <math>\varepsilon_0</math> is the [[electric constant]].
 
The vector form of Coulomb's law is simply the scalar definition of the law with the direction given by the [[unit vector]], <math>\boldsymbol{\hat{r}_{21}}</math>, parallel with the line ''from'' charge <math>q_2</math> ''to'' charge <math>q_1</math>.<ref name="uTexas">[http://farside.ph.utexas.edu/teaching/em/lectures/node28.html Coulomb's law], University of Texas</ref> If both charges have the same [[Plus and minus signs|sign]] (like charges) then the [[Scalar multiplication|product]] <math>q_1q_2</math> is positive and the direction of the force on <math>q_1</math> is given by <math>\boldsymbol{\hat{r}_{21}}</math>; the charges repel each other. If the charges have opposite signs then the product <math>q_1q_2</math> is negative and the direction of the force on <math>q_1</math> is given by <math>-\boldsymbol{\hat{r}_{21}}</math>; the charges attract each other.
 
The electrostatic force <math>\boldsymbol{F_2}</math> experienced by <math>q_2</math>, according to [[Newton's laws of motion|Newton's third law]], is <math>\boldsymbol{F_2}=-\boldsymbol{F_1}</math>.
 
===System of discrete charges===
The [[superposition principle|law of superposition]] allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the [[vector addition]] of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the [[electric field]] vector at that point, with that point charge removed.
 
The force <math>\boldsymbol{F}</math> on a small charge, <math>q</math> at position <math>\boldsymbol{r}</math>, due to a system of <math>N</math> discrete charges in vacuum is:
 
:<math>\boldsymbol{F(r)}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{r-r_i}\over|\boldsymbol{r-r_i}|^3}={q\over4\pi\varepsilon_0}\sum_{i=1}^Nq_i{\boldsymbol{\widehat{R_i}}\over|\boldsymbol{R_i}|^2},</math>
 
where <math>q_i</math> and <math>\boldsymbol{r_i}</math> are the magnitude and position respectively of the <math>i^{th}</math> charge, <math>\boldsymbol{\widehat{R_i}}</math> is a unit vector in the direction of <math>\boldsymbol{R}_{i} = \boldsymbol{r} - \boldsymbol{r}_i</math> (a vector pointing from charges <math>q_i</math> to <math>q</math>).<ref name="uTexas"/>
 
===Continuous charge distribution===
In this case, the principle of [[linear superposition]] is also used. For a continuous charge distribution, an [[integral]] over the region containing the charge is equivalent to an infinite summation, treating each [[infinitesimal]] element of space as a point charge <math>dq</math>. The distribution of charge is usually linear, surface or volumetric.
 
For a linear charge distribution (a good approximation for charge in a wire) where <math>\lambda(\boldsymbol{r'})</math> gives the charge per unit length at position <math>\boldsymbol{r'}</math>, and <math>dl'</math> is an infinitesimal element of length,
 
:<math>dq = \lambda(\boldsymbol{r'})dl'</math>.<ref>[http://dev.physicslab.org/Document.aspx?doctype=3&filename=Electrostatics_ContinuousChargedRod.xml Charged rods], PhysicsLab.org</ref>
 
For a surface charge distribution (a good approximation for charge on a plate in a parallel plate [[capacitor]]) where <math>\sigma(\boldsymbol{r'})</math> gives the charge per unit area at position <math>\boldsymbol{r'}</math>, and <math>dA'</math> is an infinitesimal element of area,
 
:<math>dq = \sigma(\boldsymbol{r'})\,dA'.</math>
 
For a volume charge distribution (such as charge within a bulk metal) where <math>\rho(\boldsymbol{r'})</math> gives the charge per unit volume at position <math>\boldsymbol{r'}</math>, and <math>dV'</math> is an infinitesimal element of volume,
 
:<math>dq = \rho(\boldsymbol{r'})\,dV'.</math><ref name="uTexas"/>
 
The force on a small test charge <math>q'</math> at position <math>\boldsymbol{r}</math> in vacuum is given by the integral over the distribution of charge:
 
:<math>\boldsymbol{F} = {q'\over 4\pi\varepsilon_0}\int dq {\boldsymbol{r} - \boldsymbol{r'} \over |\boldsymbol{r} - \boldsymbol{r'}|^3}.</math>
 
== Simple experiment to verify Coulomb's law ==
 
[[File:Verificacion ley coulomb.png|framed|250px|thumb|Experiment to verify Coulomb's law.]]
 
It is possible to verify Coulomb's law with a simple experiment. Let's consider two small spheres of mass <math>m</math> and same-sign charge <math>q</math>, hanging from two ropes of negligible mass of length <math>l</math>. The forces acting on each sphere are three: the weight <math>m g</math>, the rope tension <math>T</math> and the electric force <math>\boldsymbol{F}</math>.
 
In the equilibrium state:
{{NumBlk||
:<math>T \ \sin \theta_1 =F_1 \,\!</math>
|{{EquationRef|1}}}}
 
and:
{{NumBlk||
:<math>T \ \cos \theta_1 =mg \,\!</math>
|{{EquationRef|2}}}}
 
Dividing ({{EquationNote|1}}) by ({{EquationNote|2}}):
{{NumBlk||
:<math>\frac {\sin \theta_1}{\cos \theta_1 }=
\frac {F_1}{mg}\Rightarrow F_1= mg \tan \theta_1 </math>
|{{EquationRef|3}}}}
 
Being <math>L_1 \,\!</math> the distance between the charged spheres; the repulsion force between them <math>F_1 \,\!</math>, assuming Coulomb's law is correct, is equal to
{{NumBlk||
<math> F_1 = \frac{q^2}{4 \pi \epsilon_0 L_1^2}</math>
|{{EquationRef|Coulomb's law}}}}
 
so:
{{NumBlk||
<math>\frac{q^2}{4 \pi \epsilon_0 L_1^2}=mg \tan \theta_1 \,\!</math>
|{{EquationRef|4}}}}
 
If we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge ''q''/2. In the equilibrium state, the distance between the charges will be <math>L_2<L_1 \,\!</math> and the repulsion force between them will be:
{{NumBlk||
:<math>F_2 = \frac{{(q/2)}^2}{4 \pi \epsilon_0 L_2^2}=\frac{q^2/4}{4 \pi \epsilon_0 L_2^2} \,\!</math>
|{{EquationRef|5}}}}
 
We know that <math>F_2= mg. \tan \theta_2 \,\!</math>. And:
:<math>\frac{\frac{q^2}{4}}{4 \pi \epsilon_0 L_2^2}=mg. \tan \theta_2</math>
 
Dividing ({{EquationNote|3}}) by ({{EquationNote|4}}), we get:
{{NumBlk||
:<math>\frac{\left( \cfrac{q^2}{4 \pi \epsilon_0 L_1^2} \right)}{\left(\cfrac{q^2/4}{4 \pi \epsilon_0 L_2^2}\right)}=
\frac{mg \tan \theta_1}{mg \tan \theta_2}
\Longrightarrow 4 {\left ( \frac {L_2}{L_1} \right ) }^2=
\frac{ \tan \theta_1}{ \tan \theta_2}</math>
|{{EquationRef|6}}}}
 
Measuring the angles <math>\theta_1 \,\!</math> and <math>\theta_2 \,\!</math> and the distance between the charges <math>L_1 \,\!</math> and <math>L_2 \,\!</math> is sufficient to verify that the equality is true, taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation:
{{NumBlk||
:<math>\tan \theta \approx \sin \theta= \frac{\frac{L}{2}}{l}=\frac{L}{2l}\Longrightarrow\frac{ \tan \theta_1}{ \tan \theta_2}\approx \frac{\frac{L_1}{2l}}{\frac{L_2}{2l}}</math>
|{{EquationRef|7}}}}
 
Using this approximation, the relationship ({{EquationNote|6}}) becomes the much simpler expression:
{{NumBlk||
:<math>\frac{\frac{L_1}{2l}}{\frac{L_2}{2l}}\approx 4 {\left ( \frac {L_2}{L_1} \right ) }^2 \Longrightarrow \,\!</math> <math>\frac{L_1}{L_2}\approx 4 {\left ( \frac {L_2}{L_1} \right ) }^2\Longrightarrow \frac{L_1}{L_2}\approx\sqrt[3]{4} \,\!</math>
|{{EquationRef|8}}}}
 
In this way, the verification is limited to measuring the distance between the charges and check that the division approximates the theoretical value.
 
== Tentative evidence of infinite speed of propagation ==
In late 2012, experimenters of the [[Istituto Nazionale di Fisica Nucleare]], at the Laboratori Nazionali di Frascati in [[Frascati]], [[Rome]] performed an experiment which indicated that there was no delay in propagation of the force between a beam of [[electron]]s and detectors.<ref name=arxiv>{{Cite arxiv | eprint=1211.2913 | last1=Calcaterra | first1=A. | last2=de Sangro | first2=R. | last3=Finocchiaro | first3=G. | last4=Patteri | first4=P. | last5=Piccolo | first5=M. | last6=Pizzella | first6=G. | title=Measuring Propagation Speed of Coulomb Fields | class=gr-qc | year=2012 }}</ref> This was taken as indicating that the field seemed to travel with the beam of electrons as if it were a rigid structure preceding the beam. Though awaiting corroboration, the results indicate that [[aberration]] is not present in the Coulomb force.
 
==Electrostatic approximation==
In either formulation, Coulomb’s law is fully accurate only when the objects are stationary, and remains approximately correct only for slow movement. These conditions are collectively known as the [[electrostatics#Electrostatic approximation|electrostatic approximation]]. When movement takes place, [[magnetic field]]s that alter the force on the two objects are produced. The magnetic interaction between moving charges may be thought of as a manifestation of the force from the electrostatic field but with [[Albert Einstein|Einstein]]’s [[theory of relativity]] taken into consideration. Other theories like [[Weber electrodynamics]] predict other velocity-dependent corrections to Coulomb's law.
 
===Atomic forces===
Coulomb's law holds even within [[atom]]s, correctly describing the [[force]] between the positively charged [[atomic nucleus]] and each of the negatively charged [[electron]]s. This simple law also correctly accounts for the forces that bind atoms together to form [[molecule]]s and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between [[ion]]s increases, the energy of attraction approaches zero and [[ionic bonding]] is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable.
 
==See also==
{{Portal|Electronics}}
* [[Biot–Savart law]]
* [[Method of image charges]]
* [[Electromagnetic force]]
* [[Molecular modelling]]
* [[Static forces and virtual-particle exchange]]
* [[Darwin Lagrangian]]
* [[Newton's Law of Universal Gravitation]], which uses a similar structure, but for mass instead of charge.
 
==References==
*{{cite book | last=Coulomb |first=Charles Augustin | title=Histoire de l’Académie Royale des Sciences |year=1788 |publisher = Imprimerie Royale |chapter=Premier mémoire sur l’électricité et le magnétisme |pages=569–577 |origyear=1785 |chapterurl=http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA569#v=onepage&q&f=false}}
*{{cite book | last=Coulomb |first=Charles Augustin | title=Histoire de l’Académie Royale des Sciences |year=1788 |publisher = Imprimerie Royale |chapter=Second mémoire sur l’électricité et le magnétisme |pages=578–611 |origyear=1785 |chapterurl=http://books.google.com/books?id=by5EAAAAcAAJ&pg=PA578#v=onepage&q&f=false}}
* {{cite book | author=Griffiths, David J.|title=Introduction to Electrodynamics |edition=3rd | publisher=Prentice Hall |year=1998 |isbn=0-13-805326-X}}
* {{cite book | last1=Tipler | first1=Paul A. | last2=Mosca | first2=Gene | title=Physics for Scientists and Engineers |edition=6th | publisher=W. H. Freeman and Company |location=New York | year=2008 | isbn=0-7167-8964-7 | lccn=2007010418}}
* {{cite book | last1= Young |first1 = Hugh D. | last2 = Freedman| first2 = Roger A. | title = Sears and Zemansky's University Physics : With Modern Physics| edition = 13th| year = 2010| publisher = Addison-Wesley (Pearson)| isbn = 978-0-321-69686-1}}

Latest revision as of 17:47, 21 October 2013

Earlier than you determine whether or not stainless steel cookware is value shopping for, lets first talk about what stainless steel cookware is. Chrome steel is made from an alloy, or a mix of metals. Mostly, fundamental iron with chromium, nickel or some other minor metals. The chromium supplies rust protection and provides your cookware sturdiness. The nickel provides rust safety as effectively, and provides a refined look. Most effectively made chrome steel cookware has copper or aluminum added to the underside of the pan or pot. This is finished to increases the ability of the pot or pan to conduct heat.
One of the best stainless-steel cookware is the principle category, however nonetheless it is divided into several subcategories based mostly on the quality and the price range. It may be confusing to decide on the very best stainless-steel cookware out of the categories that may meet your requirements. That is where we took a step forward to explain you all the knowledge that will likely be helpful so that you can understand how to decide on the best chrome steel cookware. The best stainless-steel cookware set is manufactured from low-cost to expensive and quality constructed pots and pans.
You will find magnetic stainless steel within the layer on the outside of some high quality pieces of stainless-steel. That is to make it compatible with induction stovetops, which involve using a rapidly charging electromagnetic subject to warmth cookware. High-high quality stainless steel, like All-Clad , uses three layers of steel—the austenite layer of metal on the within, ferrite steel on the outside, and a layer of aluminum sandwiched between the two for optimum heat conductivity (metal alone doesn't conduct warmth evenly). Lesser-high quality stainless-steel is usually only one layer of austenitic chrome steel.
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Arduous-anodized aluminum cookware is among the most popular forms of material, despite the fact that many people do not fairly perceive the development. Hard-anodized aluminum is plain aluminum that has been processed in a series of chemical baths charged with an electrical present. The result's a fabric that has the same superior warmth conductivity as aluminum however is non-reactive with acidic meals, similar to tomatoes, and twice as hard as chrome steel. Two drawbacks to laborious-anodized cookware are that it's not dishwasher-secure and, because it isn't magnetic, it will not work with induction range tops.
The enamel over metal method creates a piece that has the heat distribution of carbon steel and a non-reactive, low-stick surface. In the event you loved this information and you desire to acquire details about best stainless steel cookware i implore you to pay a visit to our page. Such pots are a lot lighter than most different pots of comparable dimension, are cheaper to make than chrome steel pots, and would not have the rust and reactivity problems with forged iron or carbon steel. quotation needed Enamel over metal is right for large stockpots and for different giant pans used mostly for water-primarily based cooking. Because of its mild weight and simple cleanup, enamel over metal can also be standard for cookware used while tenting. Clad aluminium or copper edit
Unique specialty cookware items served a la carte to compliment any cookware set are constructed of a sturdy Stainless Steel with a brushed exterior finish. Designed with an impression bonded, aluminum disk encapsulated base which distributes warmth quickly and evenly to permit exact temperature management. Handles are riveted for durability and efficiency. The New Specialty Cookware is compatible for all vary sorts together with induction. Along with the multi use function, another unique characteristic is bottom to top interior quantity markings in each quarts and metric measurement; and each bit comes with a tempered glass lid, oven safe to 350°F.
Whether or not you are a cooking enthusiasts, knowledgeable chef or simply cooking for your family you know the importance of getting a totally stocked kitchen. Not solely do you want the fitting elements, but you also need the right instruments to get the job performed. In any sort of fundamental cooking coaching lesson, you will be taught that chrome steel is your new finest pal when it comes to kitchen cookware. What additionally, you will study is that quality cooking tools does not normally come at a reduced price. Because of this, you will need to take good care of your cookware! Listed here are some fundamentals for stainless steel care.
To combat the uneven heating downside, most stainless steel pans are laminations of aluminum or copper on the underside to spread the warmth around, and stainless-steel contained in the pan to provide a cooking floor that's impervious to whatever you might put inside. In my experience, this chrome steel floor continues to be too sticky to fry on, and when you ever burn it you get a permanent hassle spot. But, sometimes a stainless-steel cooking surface turns out to be useful when you can't use aluminum (see below) so I keep some round. Choose one thing with a fairly thick aluminum layer on the underside.
Well, until you’re a metals professional and go examine the factory where the steel is made to see whether or not their manufacturing course of creates a pure austenite without corrosive supplies shaped, you’re not going to know for sure whether or not the craftsmanship of your stainless is of the very best quality. I think your greatest wager is to simply buy high-quality chrome steel from the start, from a brand with a reputation for good quality. But, I believe I have found out one way that you would be able to decide if the stainless cookware you already have is probably reactive.

Coulomb's law, or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa. The law has been tested heavily, and all observations have upheld the law's principle.

History

Charles Augustin de Coulomb

Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BC, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing.[1][2] Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber.[1] He coined the New Latin word electricus ("of amber" or "like amber", from ήλεκτρον [elektron], the Greek word for "amber") to refer to the property of attracting small objects after being rubbed.[3] This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646.[4]

Early investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli[5] and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Franz Aepinus who supposed the inverse-square law in 1758.[6]

Based on experiments with electrically charged spheres, Joseph Priestley of England was among the first to propose that electrical force followed an inverse-square law, similar to Newton's law of universal gravitation. However, he did not generalize or elaborate on this.[7] In 1767, he conjectured that the force between charges varied as the inverse square of the distance.[8][9]

Coulomb’s torsion balance

In 1769, Scottish physicist John Robison announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x-2.06.[10]

In the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England.[11]

Finally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism.[12] He used a torsion balance to study the repulsion and attraction forces of charged particles, and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law.

The law

Coulomb's law states that:

The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them.[12]
The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.
A graphical representation of Coulomb's law
A graphical representation of Coulomb's law

Template:External media

Coulomb's law can also be stated as a simple mathematical expression. The scalar and vector forms of the mathematical equation are

|F|=ke|q1q2|r2 and F1=keq1q2|r21|2r^21, respectively,

where ke is Coulomb's constant (ke=8.9875517873681764×109Nm2C2), q1 and q2 are the signed magnitudes of the charges, the scalar r is the distance between the charges, the vector r21=r1r2 is the vectorial distance between the charges, and r^21=r21/|r21| (a unit vector pointing from q2 to q1). The vector form of the equation calculates the force F1 applied on q1 by q2. If r12 is used instead, then the effect on q2 can be found. It can be also calculated using Newton's third law: F2=F1.

Units

Electromagnetic theory is usually expressed using the standard SI units. Force is measured in newtons, charge in coulombs, and distance in metres. Coulomb's constant is given by ke=1/(4πε0ε). The constant ε0 is the permittivity of free space in C2 m−2 N−1. And ε is the relative permittivity of the material in which the charges are immersed, and is dimensionless.

The SI derived units for the electric field are volts per meter, newtons per coulomb, or tesla meters per second.

Coulomb's law and Coulomb's constant can also be interpreted in various terms:

  • Atomic units. In atomic units the force is expressed in hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius.
  • Electrostatic units or Gaussian units. In electrostatic units and Gaussian units, the unit charge (esu or statcoulomb) is defined in such a way that the Coulomb constant Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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Electric field

If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.

An electric field is a vector field that associates to each point in space the Coulomb force experienced by a test charge. In the simplest case, the field is considered to be generated solely by a single source point charge. The strength and direction of the Coulomb force F on a test charge qt depends on the electric field E that it finds itself in, such that F=qtE. If the field is generated by a positive source point charge q, the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge qt would move if placed in the field. For a negative point source charge, the direction is radially inwards.

The magnitude of the electric field E can be derived from Coulomb's law. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field E created by a single source point charge q at a certain distance from it r in vacuum is given by:

|E|=14πε0|q|r2.

Coulomb's constant

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

Coulomb's constant is a proportionality factor that appears in Coulomb's law as well as in other electric-related formulas. Denoted ke, it is also called the electric force constant or electrostatic constant, hence the subscript e.

The exact value of Coulomb's constant is:

ke=14πε0=c02μ04π=c02×107Hm1=8.9875517873681764×109Nm2C2

Conditions for validity

There are two conditions to be fulfilled for the validity of Coulomb’s law:

  1. The charges considered must be point charges.
  2. They should be stationary with respect to each other.

Scalar form

The absolute value of the force F between two point charges q and Q relates to the distance between the point charges and to the simple product of their charges. The diagram shows that like charges repel each other, and opposite charges attract each other.

When it is only of interest to know the magnitude of the electrostatic force (and not its direction), it may be easiest to consider a scalar version of the law. The scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force F acting simultaneously on two point charges q1 and q2 as follows:

|F|=ke|q1q2|r2

where r is the separation distance and ke is Coulomb's constant. If the product q1q2 is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive.[13]

Vector form

In the image, the vector F1 is the force experienced by q1, and the vector F2 is the force experienced by q2. When q1q2>0 the forces are repulsive (as in the image) and when q1q2<0 the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.

Coulomb's law states that the electrostatic force F1 experienced by a charge, q1 at position r1, in the vicinity of another charge, q2 at position r2, in a vacuum is equal to:

F1=q1q24πε0(r1r2)|r1r2|3=q1q24πε0r^21|r21|2,

where r21=r1r2, the unit vector r^21=r21/|r21|, and ε0 is the electric constant.

The vector form of Coulomb's law is simply the scalar definition of the law with the direction given by the unit vector, r^21, parallel with the line from charge q2 to charge q1.[14] If both charges have the same sign (like charges) then the product q1q2 is positive and the direction of the force on q1 is given by r^21; the charges repel each other. If the charges have opposite signs then the product q1q2 is negative and the direction of the force on q1 is given by r^21; the charges attract each other.

The electrostatic force F2 experienced by q2, according to Newton's third law, is F2=F1.

System of discrete charges

The law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed.

The force F on a small charge, q at position r, due to a system of N discrete charges in vacuum is:

F(r)=q4πε0i=1Nqirri|rri|3=q4πε0i=1NqiRi^|Ri|2,

where qi and ri are the magnitude and position respectively of the ith charge, Ri^ is a unit vector in the direction of Ri=rri (a vector pointing from charges qi to q).[14]

Continuous charge distribution

In this case, the principle of linear superposition is also used. For a continuous charge distribution, an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge dq. The distribution of charge is usually linear, surface or volumetric.

For a linear charge distribution (a good approximation for charge in a wire) where λ(r) gives the charge per unit length at position r, and dl is an infinitesimal element of length,

dq=λ(r)dl.[15]

For a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where σ(r) gives the charge per unit area at position r, and dA is an infinitesimal element of area,

dq=σ(r)dA.

For a volume charge distribution (such as charge within a bulk metal) where ρ(r) gives the charge per unit volume at position r, and dV is an infinitesimal element of volume,

dq=ρ(r)dV.[14]

The force on a small test charge q at position r in vacuum is given by the integral over the distribution of charge:

F=q4πε0dqrr|rr|3.

Simple experiment to verify Coulomb's law

Experiment to verify Coulomb's law.

It is possible to verify Coulomb's law with a simple experiment. Let's consider two small spheres of mass m and same-sign charge q, hanging from two ropes of negligible mass of length l. The forces acting on each sphere are three: the weight mg, the rope tension T and the electric force F.

In the equilibrium state: Template:NumBlk

and: Template:NumBlk

Dividing (Template:EquationNote) by (Template:EquationNote): Template:NumBlk

Being L1 the distance between the charged spheres; the repulsion force between them F1, assuming Coulomb's law is correct, is equal to Template:NumBlk

so: Template:NumBlk

If we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge q/2. In the equilibrium state, the distance between the charges will be L2<L1 and the repulsion force between them will be: Template:NumBlk

We know that F2=mg.tanθ2. And:

q244πϵ0L22=mg.tanθ2

Dividing (Template:EquationNote) by (Template:EquationNote), we get: Template:NumBlk

Measuring the angles θ1 and θ2 and the distance between the charges L1 and L2 is sufficient to verify that the equality is true, taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation: Template:NumBlk

Using this approximation, the relationship (Template:EquationNote) becomes the much simpler expression: Template:NumBlk

In this way, the verification is limited to measuring the distance between the charges and check that the division approximates the theoretical value.

Tentative evidence of infinite speed of propagation

In late 2012, experimenters of the Istituto Nazionale di Fisica Nucleare, at the Laboratori Nazionali di Frascati in Frascati, Rome performed an experiment which indicated that there was no delay in propagation of the force between a beam of electrons and detectors.[16] This was taken as indicating that the field seemed to travel with the beam of electrons as if it were a rigid structure preceding the beam. Though awaiting corroboration, the results indicate that aberration is not present in the Coulomb force.

Electrostatic approximation

In either formulation, Coulomb’s law is fully accurate only when the objects are stationary, and remains approximately correct only for slow movement. These conditions are collectively known as the electrostatic approximation. When movement takes place, magnetic fields that alter the force on the two objects are produced. The magnetic interaction between moving charges may be thought of as a manifestation of the force from the electrostatic field but with Einstein’s theory of relativity taken into consideration. Other theories like Weber electrodynamics predict other velocity-dependent corrections to Coulomb's law.

Atomic forces

Coulomb's law holds even within atoms, correctly describing the force between the positively charged atomic nucleus and each of the negatively charged electrons. This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the energy of attraction approaches zero and ionic bonding is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable.

See also

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References

  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  1. 1.0 1.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  2. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  3. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  4. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  5. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  6. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  7. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  8. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

    May we not infer from this experiment, that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated, that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?

  9. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  10. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
    On page 68, the author states that in 1769 he announced his findings regarding the force between spheres of like charge. On page 73, the author states the force between spheres of like charge varies as x-2.06:

    The result of the whole was, that the mutual repulsion of two spheres, electrified positively or negatively, was very nearly in the inverse proportion of the squares of the distances of their centres, or rather in a proportion somewhat greater, approaching to x-2.06.

    When making experiments with charged spheres of opposite charge the results were similar, as stated on page 73:

    When the experiments were repeated with balls having opposite electricities, and which therefore attracted each other, the results were not altogether so regular and a few irregularities amounted to 1/6 of the whole; but these anomalies were as often on one side of the medium as on the other. This series of experiments gave a result which deviated as little as the former (or rather less) from the inverse duplicate ratio of the distances; but the deviation was in defect as the other was in excess.

    Nonetheless, on page 74 the author infers that the actual action is related exactly to the inverse duplicate of the distance:

    We therefore think that it may be concluded, that the action between two spheres is exactly in the inverse duplicate ratio of the distance of their centres, and that this difference between the observed attractions and repulsions is owing to some unperceived cause in the form of the experiment.

    On page 75, the authour compares the electric and gravitational forces:

    Therefore we may conclude, that the law of electric attraction and repulsion is similar to that of gravitation, and that each of those forces diminishes in the same proportion that the square of the distance between the particles increases.

  11. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
    On pages 111 and 112 the author states:

    We may therefore conclude that the electric attraction and repulsion must be inversely as some power of the distance between that of the 2 + 1/50 th and that of the 2 - 1/50 th, and there is no reason to think that it differs at all from the inverse duplicate ratio.

  12. 12.0 12.1 In -- Coulomb (1785a) "Premier mémoire sur l’électricité et le magnétisme," Histoire de l’Académie Royale des Sciences, pages 569-577 -- Coulomb studied the repulsive force between bodies having electrical charges of the same sign:

    Page 574 : Il résulte donc de ces trois essais, que l'action répulsive que les deux balles électrifées de la même nature d'électricité exercent l'une sur l'autre, suit la raison inverse du carré des distances.

    Translation : It follows therefore from these three tests, that the repulsive force that the two balls --[that were] electrified with the same kind of electricity -- exert on each other, follows the inverse proportion of the square of the distance.

    In -- Coulomb (1785b) "Second mémoire sur l’électricité et le magnétisme," Histoire de l’Académie Royale des Sciences, pages 578-611. -- Coulomb showed that oppositely charged bodies obey an inverse-square law of attraction.
  13. Coulomb's law, Hyperphysics
  14. 14.0 14.1 14.2 Coulomb's law, University of Texas
  15. Charged rods, PhysicsLab.org
  16. Template:Cite arxiv