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Coulomb's law
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Coulomb's law is a law of physics describing the electrostatic interaction between
electrically charged particles. It was studied and first published in 1783 by French
physicist Charles Augustin de Coulomb and was essential to the development of the
theory of electromagnetism. Nevertheless, the dependence of the electric force with
distance (inverse square law) had been proposed previously by Joseph Priestley[1] and
the dependence with both distance and charge had been discovered, but not published, by
Henry Cavendish, prior to Coulomb's works.
Coulomb's law may be stated in scalar form as follows:
The magnitude of the electrostatic force between two point electric charges is directly
proportional to the product of the magnitudes of each of the charges and inversely
proportional to the square of the distance between the two charges.
Contents
[hide]
1 Scalar form
1.1 Electric field
2 Vector form
2.1 System of discrete charges
2.2 Continuous charge distribution
2.3 Graphical representation
3 Electrostatic approximation
4 Table of derived quantities
5 See also
6 Notes
7 References
8 External links
[edit] Scalar form
Diagram describing the basic mechanism of Coulomb's law; like charges repel each other
and opposite charges attract each other.
Coulomb's torsion balance
The scalar form of Coulomb's law will only describe the magnitude of the electrostatic
force between two electric charges. If direction is required, then the vector form is
required as well. The magnitude of the electrostatic force (F) on a charge (q1) due to the
presence of a second charge (q2), is given by
where r is the distance between the two charges and ke a proportionality constant. A
positive force implies a repulsive interaction, while a negative force implies an attractive
interaction.[2]
The proportionality constant ke, called the Coulomb constant (sometimes called the
Coulomb force constant), is related to defined properties of space and can be calculated
exactly:[3]
By definition in SI units, the speed of light in vacuum, denoted c,[4] is
299,792,458 m·s−1,[5] and the magnetic constant (μ0), is defined as 4π × 10−7
H·m−1,[6] leading to the consequential defined value for the electric constant (ε0) as ε0 =
1/(μ0c2) ≈ 8.854187817×10−12 F·m−1.[7] In cgs units, the unit charge, esu of charge or
statcoulomb, is defined so that this Coulomb constant is 1 and dimensionless.
This formula says that the magnitude of the force is directly proportional to the
magnitude of the charges of each object and inversely proportional to the square of the
distance between them. The exponent in Coulomb's Law has been found to be equal to −2
with precision of at least 2.7±3.1×10−16.[8]
Coulomb's law can also be interpreted in terms of atomic units with the force expressed
in Hartrees per Bohr radius, the charge in terms of the elementary charge, and the
distances in terms of the Bohr radius.
[edit] Electric field
Main article: Electric field
It follows from the Lorentz Force Law that the magnitude of the electric field (E) created
by a single point charge (q) at a certain distance (r) is given by:
For a positive charge, the direction of the electric field points along lines directed radially
away from the location of the point charge, while the direction is the opposite for a
negative charge. The SI units of electric field are volts per metre or newtons per coulomb.
[edit] Vector form
In order to obtain both the magnitude and direction of the force on a charge, q1 at
position , experiencing a field due to the presence of another charge, q2 at position ,
the full vector form of Coulomb's law is required.
where r is the separation of the two charges. This is simply the scalar definition of
Coulomb's law with the direction given by the unit vector,
, parallel with the line from
charge q2 to charge q1.[9]
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
; 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
; the charges attract each other.
[edit] System of discrete charges
The principle of linear superposition may be used to calculate the force on a small test
charge, q, due to a system of N discrete charges:
where qi and are the magnitude and position respectively of the ith charge,
is a unit
vector in the direction of
(a vector pointing from charge qi to charge q),
and Ri is the magnitude of
(the separation between charges qi and q).[9]
[edit] Continuous charge distribution
For a 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.
For a linear charge distribution (a good approximation for charge in a wire) where
gives the charge per unit length at position , and
is an infinitesimal element of
length,
.[10]
For a surface charge distribution (a good approximation for charge on a plate in a parallel
plate capacitor) where
gives the charge per unit area at position
infinitesimal element of area,
, and
is an
For a volume charge distribution (such as charge within a bulk metal) where
gives
the charge per unit volume at position , and
is an infinitesimal element of volume,
[9]
The force on a small test charge
at position is given by
[edit] Graphical representation
Below is a graphical representation of Coulomb's law, when q1q2 > 0. The vector
is
the force experienced by q1. The vector
is the force experienced by q2. Their
magnitudes will always be equal. The vector
is the displacement vector between two
charges (q1 and q2).
A graphical representation of Coulomb's law.
[edit] 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 are produced which alter the force on the two objects. 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.
[edit] Table of derived quantities
Particle property
Relationship
Field property
Force (on 1 by 2)
Electric field (at 1 by
2)
Potential energy (at 1
by 2)
Potential (at 1 by 2)
Vector
quantity
Relationshi
p
Scalar
quantity
[edit] See also
Electronics portal
Biot–Savart law
Method of image charges
Electric field
Electric constant
Coulomb, the SI unit of electric charge named after Charles Augustin de Coulomb
Electromagnetic force
Molecular modelling
Static forces and virtual-particle exchange
Darwin Lagrangian
[edit] Notes
^ Robert S. Elliott (1999). Electromagnetics: History, Theory, and Applications.
ISBN 978-0-7803-5384-8. http://eu.wiley.com/WileyCDA/WileyTitle/productCd0780353846.html
^ Coulomb's law, Hyperphysics
^ Coulomb's constant, Hyperphysics
^ Current practice is to use c0 to denote the speed of light in vacuum according to ISO
31. In the original Recommendation of 1983, the symbol c was used for this purpose and
continues to be commonly used. See NIST Special Publication 330, Appendix 2, p. 45
^ [1]
^ [2]
^ http://physics.nist.gov/cgi-bin/cuu/Value?ep0
^ Williams, Faller, Hill, E.; Faller, J.; Hill, H. (1971). "New Experimental Test of
Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass". Physical Review
Letters 26: 721–724. doi:10.1103/PhysRevLett.26.721.
http://prola.aps.org/abstract/PRL/v26/i12/p721_1
^ a b c Coulomb's law, University of Texas
^ Charged rods, PhysicsLab.org
[edit] References
Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall.
ISBN 0-13-805326-X.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light,
and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
[edit] External links
Coulomb's Law on Project PHYSNET.
Electricity and the Atom — a chapter from an online textbook
A maze game for teaching Coulomb's Law—a game created by the Molecular
Workbench software
The inverse cube law The inverse cube law for dipoles (PDF file) by Eng. Xavier Borg
Electric Charges, Polarization, Electric Force, Coulomb's Law Walter Lewin, 8.02
Electricity and Magnetism, Spring 2002: Lecture 1 (video). MIT OpenCourseWare.
License: Creative Commons Attribution-Noncommercial-Share Alike.
Retrieved from "http://en.wikipedia.org/wiki/Coulomb%27s_law"
Categories: Electrostatics | Introductory physics | Fundamental physics concepts
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