Electrostatics - Coulomb law
The basic law of electrostatics was formulated by Coulomb. Assuming that we have very small charged particles which can be treated as points, Coulomb’s law says:
The force between two charged particles is directly proportional to the product of the charges on these particles and inversely proportional to the square of the distance between them and acts along a straight line joining the centers of these particles.
Fig.1 will help in the precise formulation of this law.
According to the annotation on Fig.1 the mathematical formulation of Coulomb’s law is
(1)
The value of the coefficient of proportionality k depends on the medium in which the electric charges interact and on the choice of units. We consequently use SI units and for charges interacting in vacuum ( or in dry air)
(2)
where ε0 is called the permittivity of vacuum and ε0 = 8.85 x10-12 C2/Nm2. Just to remind you - N stands for unit of force Newton. The value of the permittivity of dry air is so close to that of a vacuum that we will treat experiments in the air as performed in a vacuum.
So, for the vacuum and for the air we will use the same numerical value
k = 8.99x109 Nm2/C2.
Values of ε0 and consequently of k have been determined with much greater accuracy, but for solving problems there is no need to use these very accurate values.
Particles with charges of the same sign experience forces away from each other while particles with charges of different signs experience forces towards each other. The signs of the charges are a relative method of distinguishing two types of charges.
If the interaction of charges takes place in a medium other than vacuum/air the proportionality coefficient
(2a)
where εr is the relative permittivity of that medium. It is defined as the ratio of the force in vacuum to the force in any other medium between the same pair of charges separated by the same distance r. The relative permittivity εr is greater than 1 for any medium other than vacuum/air.
This relative permittivity enters into the denominator in Coulomb’s law defined by formula (1), therefore the force acting between the charges is always smaller in any medium other than vacuum or air.
The Coulomb’s law Formula (1) is valid for point charges only. In all experiments in macroscopic scale the charges are located on objects of finite dimensions, so they are not point charges, but Coulomb’s law can be applied to these experiments if only the dimensions of the charged objects are much smaller than the distance between the centers of these objects.
The forces acting between electric charges are additive. These and many other details concerning these forces will be considered and explained in problems which you can solve like in a classroom. These problems constitute the main help in understanding physics. As mentioned in many places this physics tutorial is continuously growing because each time the author has a few hours to spare, new paragraphs are added or new problems with full explanations submitted.