Shown by experiment, an Electric Force between two stationary, charged particles is inversely proportional to the square of the separation r between the particles and is directed along the line joining the particles. The force is proportional to the product of the charges q1 and q2 on the two particles. The force is attractive if the charges are opposite in sign and repulsive if the charges are of the same sign.
These observations construct the equation for the magnitude of the electric force between the two charged particles as F = k|q1||q2|/r2, established in 1785 by Charles Coulomb and known as Coulomb's Law. The letter k here is Coulomb's Constant; Coulomb showed that the exponent of r was 2 to within an uncertainty of a few percent. Modern experiments have shown that the exponent of r is 2 with a precision of a few parts per billion.
The constant k has a value dependent upon the choice of units. The unit of Charge in the SI System is the Coulomb (C). The Coulomb is expressed in terms of a unit of Current known as the Ampère, where Current is the rate of flow of charge. When the current in a wire is 1 Ampère, the amount of charge flowing past a given point in the wire in 1 second is 1 Coulomb. Experiment gives the Coulomb Constant k in SI units as
k = 8.9875×109 N•m2/C2; k is also written as k = 1/4πε0 with ε0, the permittivity of free space, equal to
8.8542×10-12 C2/N•m2.
No unit of free charge smaller than e (±1.60219×10-19 C) has ever been detected. One Coulomb of charge equals the charge of 1/e, the amount of charge on approximately 6.3×1018 electrons. This would be close to the number of free electrons in 1 cubic centimeter of copper, about 1023 electrons. 1 Coulomb is a significant amount of charge. When a rubber or glass rod is charged by friction, a net charge around 1 millionth of a Coulomb is obtained; only a very small fraction of the total available charge passes between the rod and the material rubbed against it.
Note that force in Coulomb's Law is a vector. Note also that Coulomb's Law exactly applies only to point charges or particles. If r is taken to be a unit vector from charge q2 to charge q1, then the electric force on
q1 due to q2, F12, is equal to (kq1q2/r2)r12 with r12 a unit vector going from q1 to q2. Coulomb's Law follows Newton's Third Law, so the electric force on q2 due to q1 is equal in magnitude to the force on q1 due to q2 and is oppositely directed (F21 = -F12). For F12 = (kq1q2/r2)r12, one will have a positive (repulsive) force if q1 and q2 have the same sign and a negative (attractive) force if if q1 and q2 have opposite signs.
If more than 2 charges are present, the force between any pair of charges is given by F12 = (kq1q2/r2)r12. Therefore, the resultant force on any one of the charges is the vector sum of the forces due to the various individual charges. This principle of Superposition as applied to electrostatic forces is borne out by experiment. For four charges the resultant force on charge 1 due to charges 2, 3, and 4 would be written as
F1 = F12 + F13 + F14.
