1.2 Electrostatic: Coulomb's Law

Coulombs's Law

Coulomb measured the magnitudes of the electric forces between charged objects using the torsion balance. Coulomb’s experiments showed that the electric force between two stationary charged particles

• is inversely proportional to the square of the separation r between the particles and directed along the line joining them.

• is proportional to the product of the charges q1 and q2 on the two particles.

• is attractive if the charges are of opposite sign and repulsive if the charges have the same sign.

From these observations, we can express Coulomb’s law as an equation giving the magnitude of the electric force (sometimes called the Coulomb force) between two point charges:

where ke is a constant called the Coulomb constant. In his experiments, Coulomb was able to show that the value of the exponent of r was 2 to within an uncertainty of a few percent. Modern experiments have shown that the exponent is 2 to within an uncertainty of a few parts in 1016. The value of the Coulomb constant depends on the choice of units. The SI unit of charge is the coulomb (C). The Coulomb constant ke in SI units has the value

where the constant (epsilon) is known as the permittivity of free space.

When dealing with Coulomb’s law, you must remember that force is a vector quantity and must be treated accordingly. Thus, the law expressed in vector form for the electric force exerted by a charge q1 on a second charge q2 , written F12 , is

where is a unit vector directed from q1 to q2 ,

Because the electric force obeys Newton’s third law, the electric force exerted by q2 on q1 is equal in magnitude to the force exerted by q1 on q2 and in the opposite direction.