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Electrostatics (Read 1599 times)
Gerrit-Jan Linker
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Posts: 75
06.09.09 at 19:34:32
Electrostatics deals with the phenomena arising from stationary or slowly moving  electrons.  
Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law.
The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges.
F = q1q2/4πε0r2
or in different notation, the force of a charge qa on qb:
F(qa on qb) = (1/4πε0) q1q2  (rb-ra)/|rb-ra|3
The electric field (in units of volts per meter) at a point is defined as the force (in newtons) per unit charge (in coulombs) on a charge at that point:
F = q E  
The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational.
▼ x  E = 0  
Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage). An electric field, E, points from regions of high potential, φ, to regions of low potential.
Potential, Potential energy and Work
The 'potential' at a point is defined as the amount of work needed to bring a unit charge from infinity to that point. The potential difference between two points is then the work done to move a unit charge between these two points. The work done does not depend on the route followed so the potential is a scalar quantity. The unit of potential is the 'volt'.  
The work done on a charge qa to bring it from infinity to a distance r from qb is:
W =  -rF(r)dr = -rqaqb/4πε0r2 = -(qaqb/4πε0) rr-2 = -Cqaqb rr-2 = +(1/4πε0)qaqb r-1|r = (1/4πε0)qaqb/r
The potential energy Uab = (1/4πε0)qaqb/rab = qaΦ(r)  
where Φ(r)= (1/4πε0)qb/rab is called the potential due to qb
The force vector F is related to the scalar potential U by:
F = - grad U
For a pair of point charges this is:
Uab = (1/4πε0) q1q2  (1/|ra-rb|)
Basic Electrostatics
Chapter 0 in Modelling molecular structures, 2nd ed, Alan Hinchliffe
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« Last Edit: 23.09.11 at 14:00:03 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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