State and explain Coulomb's law of force in electrostatics. What is the S.I. unit of charge and hence define one Coulomb of charge using this law ?

Explanation

Coulomb.s Law : It, states that electrostatic force between two stationary point charges is directly proportional to the product of magnitude of two charges and inversely proportional to the square of the distance between them.
Let we have two stationary point charges `q_1 and q_2`
r = distance between `q_1and q_2`

F = Electrostatic force between `q_1 and q_2`
According to Coulomb.s law
`Fprop q_1q_2`
`F prop 1/(r^2)`
On combining (1) and (2)
`F=(q_1q_2)/(r^2)`
`F prop (q_1q_2)/r^2`
where K= Constant of proportionality
In S.I. system, `K=1/(4pi in_0) = 9 xx10^(9) Nm^2 C^(-2)`
and `in_0` = Absolute permittivity of free space `= 8.854 xx 10^(-12) C^(2) N^(-1) m^(-2)`
So `F=1/(4piin_0)(q_1q_2)/r^2`
S.I. unit of charge is Coulomb.
If `q_1 =q_2=q` (say)
r = 1 m
and `F = 9 xx10^(9) N`
Then from (3)
`9xx10^9= 9 xx10^9xxq^2/((1)^2)`
`implies q^2 =1`
`implies q =pm C`
One Coulomb is that charge which repels equal and similar charge with a force of `9 xx 10^(9)` N when these are placed 1 m apart in vacuum or air.