Coulomb force

Quite simply put, the Coulomb force is the force between charges. It was first established by Charles Augustine Coulomb¹ in 1785. Coulomb established that the force F diminished with the square of the distance r, or

F = k r^-2

with k a constant. This is exactly the same as the relation for gravity. Some people have bothered to find out whether this 2 is exactly 2, or almost 2, and the result of very accurate measurements was that differs from two by less than 1 parts in a billion.²

The next step is to find this constant k, which depends on the charge of the objects. The total form of the equation now reads

F = (q₁ q₂r^-2)/(4 π ε₀) with ε₀ the permittivity of vacuum and q the charges. The second term between brackets has a magnitude of 9.0x10⁹ N m² C ^-2 The form of the equation is again the same as the equation describing gravity. There are, however, two important differences:

• Firstly, the Coulomb force is either repulsive (like charges) or attractive (unlike charges), while the gravitational force is always attractive.
• Secondly, the constant in the Coulomb force is much higher than that in the gravitational force. This means that charges of 1 coulomb-roughly the total amount of charges in a tenth of a milligram of matter-are more than 20 orders of magnitude stronger than the gravitational attraction between 2 objects of 1 kg at the same distance.

In practice, the positive and negative charges are tightly bound, due to the large magnitude of the Coulomb force. Charges of 1 millionth of a Coulomb are already considered large. Hence, the long-distance interaction between matter is dominated by the gravitational force, while at short distances, the Coulomb force rules supreme. Indeed, it is the Coulomb force keeping ordinary objects, such as you, together.

Physically, the Coulomb force is a special case of the general electromagnetic force. The Coulomb force describes only the electrostatic part of this force. This means it is only completely valid if all the particles are standing completely still. However, it is still a good approximation if the speeds involved are much smaller than the speed of light. This last condition is often satisfied, making the Coulomb force a very useful approximation in practice.

1. http://scienceworld.wolfram.com/physics/CoulombForce.html
2. http://en.wikipedia.org/wiki/Coulomb's_law