Coulomb’s Law

 

Coulomb’s law is a quantitative statement about the force between two point charges studied by Coulomb in 1785. 

When the linear size of charged bodies are much smaller than the distance separating them, then the size may be ignored and the charged bodies are treated as point charges.

Coulomb’s law states that the forces of attraction or repulsion between two point charges is directly proportional to the product of magnitude of two charges and inversely proportional to the square of distance between them. The direction of force is along the line joining the two point charges.

Image result for coulombs law

Let the q1 and q2 be the two point charges placed in air or vacuum at a distance ‘r’ apart as shown in figure. Then, by coulomb’s law,

 

 

where k is a constant of proportionality. In air or vacuum, where is the permittivity of free space (i.e. vacuum) and the value of is 8.854 × 10-12  C2 N-1 m-2  .

                                 ------ (1)

and             = 9 × 109   N m2 C-2   .

In the above equation, if q1 = q2 = 1C and r= 1m then,

F = (9  109 ) 

    = 109 N

One coulomb is defined as the quantity of charge, which when placed at a distance of 1 meter in air or vacuum from an equal and similar charge, experiences a repulsive force 109   N.

If charges are situated in a medium of permittivity , then the magnitude of the force between them will be.,

Fm =                                     ------ (2)                   

Diving (1) by (2)             

 =  =

The ratio  = is calledrelative permittivity or dielectric constant of the medium. The value of for air or vacuum is 1.

∴                      =

Since Fm =  ,   the force of between two point charges depends on the nature of the medium in which the two charges are situated.

Coulomb's Force

Coulomb’s law- vector form:

Since force is a vector, it is better to write Coulomb’s law in the vector notation.

Image result for coulombs force vector form

Let the position vectors of charges q1 and q2 be r1 and r2 respectively.  is the force exerted by the charge q1 on charge q2. Its equation is given as

                                      ------ (3)

where  is the unit vector from q1 to q2.

 is the force exerted by the charge q2 on charge q1. Its equation is given by,

                                        ------ (4) 

Where isthe unit vectro from q2 to q1.

Here both  and  have same magnitude but are oppositely directed.

∴                  or

            or

           = -

So, the forces exerted by charges on each other are equal in magnitude and opposite in direction.