State Coulomb.s law in electrostatics and hence define units of charge in CGS (ESU) and SI system. Derive the relation between coulomb and stat-coulomb?

Explanation

Coulomb.s law in electrostatics
Units of charge in CGS (ESU) and SI system
The relation between coulomb and stat-coulomb
Let 1C=x stat-coulomb. Suppose two point charges each of q coulomb separated by a distance d metres in air.
In SI unit, Coulomb force between them is given by
`F=(1)/(4pi epsilon_(0))*(q^(2))/(d^(2)) =9 xx10^(9) xx (q^(2))/(d^(2))" newton "...(i)`
In CGS or ESU unit, Coulomb force between them is given by
`F= 1.((xq)(xq))/([10^(2)d]^(2))` dyne
`=(x^(2)q^(2))/((100d)^(2)) xx 10^(-5)N=(x^(2))/(10^(4)) (q^(2))/(d^(2)) xx 10^(-5)N`
`F=(q^(2)x^(2))/(d^(2)) xx 10^(-9) N " " ...(ii)`
On equating Eqs. (i) and (ii) , we get
`9xx10^(9) xx (q^(2))/(d^(2))= "x"^(2)(q^(2))/(d^(2))xx10^(-9)`
`rArr x^(2) =9 xx10^(9) xx10^(9) rArr x=3xx10^(9)`
Hence, `1C=3xx10^(9)` stat-coulomb