What is the definition of electric force

The Coulomb's law (after Charles Augustin de Coulomb, 1785) forms the basis of electrostatics and describes the force between two spherically symmetrically distributed electrical charges. It says that the amount of this force is proportional to the product of the two amounts of charge and inversely proportional to the square of the distance between the centers of the spheres. The direction of force acts depending on the sign of the charges attracting or repelling in the direction of the straight line connecting the center points. If there are more than two charges, the individual force vectors are added (superposition).

Coulomb force in a vacuum

Coulomb's law was discovered by Coulomb around 1785 and verified in extensive experiments. In the international system of units and in scalar form, the force is accordingly


in which q1 and q2 two spherically symmetrically distributed amounts of charge, r the distance between their centers and are the permittivity of the vacuum (electric field constant). The general vector notation gives the Coulomb force field:


Here is a unit vector in the direction of the line connecting the charge centers. The rule here is that charges with the same sign (charges of the same name) repel each other and those with different signs (charges of the same name) attract.

Next is

the vector of the field strength of the charge q1 generated electric field at a distance r from the center.

The constant

is also known as Coulomb's constant designated. The following applies:

In the Gaussian and electrostatic CGS system of units, Coulomb's law is used to define the electrical charge. One charge unit acts on a second one at a distance of 1 cm with a force of 1 dyn. The basic electrical unit of the SI, CGS-ESU and CGS-EMU unit systems only differs in the definition of µ0:

  • In the CGS-ESU is µ0 to 4π /c02 set. Therefore the Coulomb constant is a dimensionless quantity with the value 1.
  • In the CGS-EMU is µ0 set to the dimensionless size of 4π. Therefore the Coulomb constant is the same c02.

Coulomb force in a medium

The Coulomb law can easily be extended to the case of charges in homogeneous, isotropic, linear media. The material surrounding the charges must have these properties as a good approximation:

  • It is electrically neutral.
  • It fills the space between and around the charges evenly (homogeneous).
  • The polarizability of the medium is direction-independent.
  • The polarization is proportional to the electric field generated by the charges.

In particular, the homogeneity requires that the atomic character of the matter is negligible compared to the distance between the charges.

For such media, Coulomb's law is written in the same form as in a vacuum, with the only difference that ε0 by ε = ε0· Εr is replaced.

The relative permittivity εr is a material constant for isotropic media that takes into account the polarizability of the medium. It can be obtained both through measurements and from theoretical considerations.

Conversely, ε applies in a vacuumr = 1.


  • Dieter Meschede: Gerthsen physics. 23rd edition, Springer, Berlin / Heidelberg / New York 2006, ISBN 3-540-25421-8

Category: Electrostatics