Coulomb’s law:

 

Coulomb’s law:

Coulomb’s law states that the electrostatic force (F) acting between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. 

 

Suppose q₁  &  q₂    are the two point charges, separated by a distance r.

Then electrostatic force (F)  is

So we get

                     

Where  K is a proportionality constant

In SI system   K = 9 × 10⁹  Nm²C^-2

But

Where e₀ = is the electrical permittivity of space.

So

In SI system coulomb’s law is

Suppose q₁ = 1C and  q₂ = -1C, are separated by a 1m distance then electrostatic force acting between the two charge body is

F = - 9 × 10⁹ N

Here -ve sign indicates that the force is attractive,

For any other system if the sign is +ve it indicated repulsive electrostatic force.

 

Coulomb’s law in vector form

We everyone knows that force is vector means it has definite direction.  

Suppose q₁ and q₂ are two point charges, located at A and B position. Then position vector of A is

Position vector of B is

There have two possible forces

Now

Along the AB means unit vector along the AB

So

Now    

So

Expression  (1)  is called the vector form of coulomb’s law

Similarly for

We get

Expression (2) is also called vector form of coulomb’s law

 

But

that means

magnitude of BA = magnitude of AB

So                  BA³   =   AB³

Therefore from  (1) and    (2)

 

we see that

So from (1), (2), (3), and (4) we get

Be remember:

Expression  (1)   and   (2) both are the vector form of coulomb’s law