COULOMB'S LAW                         

COULOMB'S LAW 

Coulomb confirmed that the electric force between two small charged spheres is proportional to the inverse square of their separation distance r. The operating principle of the torsion balance is the same as that of the apparatus used by Cavendish to measure the gravitational constant, with the electrically neutral spheres replaced by charged ones. The electric force between charged spheres A and B causes the spheres to either attract or repel each other, and the resulting motion causes the suspended fiber to twist. Because the restoring torque of the twisted fiber is proportional to the angle through which the fiber rotates, a measurement of this angle provides a quantitative measure of the electric force of attraction or repulsion. Once the spheres are charged by rubbing, the electric force between them is very large compared with the gravitational attraction, and so the gravitational force can be neglected.

 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 10 to the power 16.

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.

This constant is also written in the form 

where the constant Eo (lowercase Greek epsilon) is known as the permittivity of free space and has the value 

 The smallest unit of charge known in nature is the charge on an electron or proton,1 which has an absolute value of 

Therefore, 1 C of charge is approximately equal to the charge of 6.24 * 10 to power18 electrons or protons. This number is very small when compared with the number of free electrons2 in 1 cm3 of copper, which is of the order of 10 TO POWER 23. Still, 1 C is a substantial amount of charge. In typical experiments in which a rubber or glass rod is charged by friction, a net charge of the order of 106 C is obtained. In other words, only a very small fraction of the total available charge is transferred between the rod and the rubbing material.

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 q 1 on a second charge q2, written F12, is

where r 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; that is, F21 = -F12. Finally, we see that if q1 and q2 have the same sign, the product q1q2 is positive and the force is repulsive. If q1 and q2 are of opposite signs, the product q1q2 is negative and the force is attractive. Noting the sign of the product q1q2 is an easy way of determining the direction of forces acting on the charges.