# Coulomb’s Law : Electric Field, Potential Difference, Volt

## What Is Coulomb's Law?

Two same types of charges repel each other and opposite types of charges attract each other. This shows that there is a force acting between two charges which is called electric force. The electric force is the repulsive force between same charges and it is the force of attraction between opposite charges.

Even if the electric charge is located in a vacuum, an electric force is applied between them.

In 1785, Francis Coulomb, on the basis of experiments, gave a rule regarding the force acting between two charges, which is called Coulomb’s law.

According to this law, “the force of attraction or repulsion between two fixed point charges is directly proportional to the product of the quantities of the two charges and inversely proportional to the square of the distance between them.” This force is along the line joining those charges.

Thus, if two point charges q1 and q2 are located at a distance r from each other, then the force between them

F ∝ q1 q2 / r2

F = k (q1 q2 / r2)

where k is a constant, whose value depends on the medium between the charges and on the units of charge, distance and force. If the unit of force is taken as newton, unit of distance is meter and unit of charge is coulomb and both the charges are located in vacuum, then by experiment, the value of k comes to 9.0 x 109.

Hence, the force between the point charges placed in a vacuum

F = 9.0 x 109 (q1 q2 / r2)

In this equation if q1 = q2 = 1 coulomb and r = 1 meter then F = 9.0 x 109. Therefore, 1 coulomb is that charge which repels an equal charge placed in vacuum at a distance of 1 meter from itself with a force of 9.0 x 109 newton. Coulomb is a very large unit of charge. In practice we use microcoulomb (μC):

1 Microcoulomb = 10-6 Coulomb

For convenience, if the point charges are located in the vacuum, the proportional constant k is written as 1/4πϵ0 in the equation.

Where 1/4πϵ0  = 9.0 x 109 Newton-meter2/coulom2 . The permittivity of free space(ε0)

If a non-conducting material is placed between the two charges in place of vecuum, then the force acting between them will be according to the following formula:

Where K is a dimensionless constant, which is called the dielectric constant or specific inductive capacity of that material and the non-conducting material is called dielectric. The value of K is greater than 1 for all dielectrics.

Therefore, if there is a dielectric between the charges, then the electric force between them decreases.

In the above formula, only e can be written in place of eK and e is called permittivity of that dielectric.

### Comparison of electric force with gravitational force

We can compare the electric force acting between two charged objects with the gravitational force acting between them. Both these forces act according to the same laws and both remain active even in vacuum. But there is also some difference between these two:

Electric force can be force of attraction as well as force of repulsion, whereas force of gravity is always force of attraction. This shows that charge can be of two types whereas mass is of only one type.

The electric force depends on the medium between the two charges whereas the gravitational force does not depend on the medium between the two masses.

The electric force is much stronger than the gravitational force. Example: The electric force between two protons is 1036 times greater than the gravitational force between them. Between two electrons it is even greater, that is, 1043 times larger.

### Importance of Coulom's law

The electric force is much stronger than the gravitational force. Example: The electric force between two protons is 1036 times greater than the gravitational force between them. Between two electrons it is even greater, that is, 1043 times larger.

Coulomb’s law is true for very large distances to very small distances, even here for atomic distances (= 10-11 meters) and nuclear distances (= 10-15 meters).

Therefore, this law not only gives knowledge of the forces acting between charged objects, but also helps to explain the forces due to which electrons of an atom bind with its nucleus to form an atom, two or more than one atom binds together to form molecules and many atoms or molecules bind together to form solids and liquids.