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# Coulomb’s Law

## Point Charges :

A charged particle whose size is very small in comparison with other distances involved in the problem is called a point charge. This is a relative concept and a large body like earth can also be considered as point object.

## Coulomb’s Law :

According to this law, the force of interaction between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. If two point charges be q1 and q2 and r is the distance between them, then,

where k is the constant of proportionality and depends on the medium in which the charges are placed and the system of units selected.

If the charges are placed in vacuum, in SI, , where e0 is the absolute permittivity of vacuum. Therefore,

From eq.(1),

Thus the unit of e0 will be,

and its value is found to be 8.854 ´ 10—12 C2 N—1 m—2

Therefore,

In vacuum and in cgs system k = 1.

Units of Charge :

In S.I., the unit of charge is Coulombs.

One Coulomb is that much charge which when placed in vacuum at a distance of 1m from an equal and similar charge would repel it with a force of 9 x 109 Newton.

In cgs system, the unit of charge is stat coulomb or e.s.u. (electrostatic unit)

1 Coulomb = 3 x 109 stat coulomb

Another unit is e.m.u. and 1 e.m.u. of charge = 1/10 Coulomb.

## Dielectric Constant or Relative Permittivity :

The force between two charges depend upon the medium between the two charges. The force between two charges q1 and q2 located at a distance r in some medium is,

where em is the absolute permittivity of that medium.

The equation (2) gives the force between charges in vacuum,

This ratio em/e0 is called relative permittivity or dielectric constant of the medium. Also, em = e0er (From 4)

Equn. (3) gives

Important Points:

1. Electrical force between two charged particles is very much stronger than the gravitational force between the charges, therefore when both the forces are present we can neglect gravitational force.
2. Electric force can be both attractive as well as repulsive whereas the gravitational force is always attractive.
3. Net electric force between charges changes with the change in medium between the charge bodies whereas the gravitational force between them is independent of the medium
4. It’s a two body interaction i.e. the electrostatic force between the charges is independent of the presence of other charges around them
5. The force is conservative in nature which implies that the work done in moving a point charge once around in closed loop is zero.