**Question 1: State and explain Coulomb’s law. Do include the case when the charges are placed in dielectrics. Discuss how the unit of charge coulomb is defined?**

ANSWER

__Coulomb’s law __

__Coulomb’s law__

French mathematician, Coulomb, studied the force between two point charges in 1785 and gave this law which states that, “two stationary charges q_{1} and q_{2} attract or repel each other with a force which;

- Is directly proportional to the scalar product q
_{1}q_{2}of the magnitudes of charges. - Is inversely proportional to the square of the distance r between them.
- Acts along the line joining the centers of the charges.”

Mathematically,

Here k is the constant of proportionality. Its value depends upon the system of units used and the medium between the two charges. The ‘electrostatic constant’ k, as it is sometimes called, is expressed in terms of permittivity of the free space ε_{0}.

Experimentally determined value of ε_{0} is 8.85 × 10^{-12} C^{2} N^{-1} m^{-2}. Therefore, putting the values of π and ε_{0},

The direction of the force is shown by a unit vector along the line joining the two charges. For like charges the product q_{1} q_{2} is positive and the force between them is repulsive. For unlike charges, the product q_{1}q_{2} is negative and the force between the charges is attractive.

It should be noted that both charges exert equal and opposite forces on one another. Therefore, if F_{21} is the force exerted by charge q_{1} on charge q_{2} and F_{12} is the force exerted by charge q_{2} on charge q_{1}, then

__When the charges are placed in a dielectric medium__

__When the charges are placed in a dielectric medium__

It has been found experimentally that when an insulator or dielectric is placed between the two point charges, the force between them decreases. In such cases, Coulomb’s force is given by,

Here ε is the permittivity of the medium.

### Relative permittivity

The ratio of the permittivity of the dielectric ε with the permittivity of vacuum ε_{0} is called relative permittivity of the dielectric or dielectric constant, ε_{r}. Therefore,

Note that ε_{r} has no dimensions.

Permittivity is the measure of the degree to which a medium can resist the flow of charge. It tells us how the magnitude of the force of the charges is affected when they are placed in a certain medium.Relative Permittivity is the permittivity of the medium compared with the (i-e, divided by) permittivity of the free space. Its value ranges from 1 to 4000 but for most material it doesn’t exceed 10. |

ε is always greater than ε_{0} and therefore ε_{r} is always greater than 1.

So the electrostatic force in a medium of relative permittivity is given by,

So the dielectric force reduces as compared to the force between the same two charges in vacuum.

__Definition of Coulomb; Unit of charge__

__Definition of Coulomb; Unit of charge__

Coulomb, the unit of charge, can be defined by considering the electrostatic force the charges exert on one another. In SI, the unit of charge is coulomb and is defined as *coulomb is that much charge which exerts on an equal and similar charge a force of repulsion of 9 × 10 ^{9} newtons placed in air at a distance of 1 meter.* In terms of current, the coulomb is defined as

*it is the charge transported by a steady current of one ampere in one second.*