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
Unit of charge in CGS (esu) and SI system
The relation between Coulomb.s and state- coulomb.s In the SI system of units.
` " " F= (1)/(4piin_0) (q^(2))/(r^(2))" "...(i)`
` " " = 9 xx 10 ^(9) (q^(2))/(r^(2))" "...(ii)`
Suppose , IC = p stat- coulomb.
Eq. (i) becomes,
` F = ((pq)(pq))/((100r)^(2)) " dyne " = (p^(2)q^(2))/(10 ^(4) r^(2)) xx 10 ^(-5) N" "...(iii)`
Comparing Eqs. (ii) and (iii) we get
` 9 xx 10 ^(9) xx ( q^(2))/(r^(2)) = (p^(2) q^(2))/(r^(2)) xx 10 ^(-9)`
` rArr " " p ^(2) = 9 xx 10 ^(18) or p =3 xx 10 ^(9)`
` rArr ` 1 Coulomb ` = 3 xx 10 ^(9)` stat - coulomb