Give the statement of Coulomb's law for the force between two point charges . Write this law in vector notation for two point charges of same magnitude and opposite sign separated by a distance r in vacuum.

Explanation

Coulomb.s Law The force of interaction (attraction or repulsion) between two stationary point charges in vacuum is directly proportional to the product of the magnitudes of two charges and inversely proportional to the square of distance between them .

`F = (1)/(4pi epsi_(0)) (q * (q))/(r^2) = (1)/(4 pi epsi_(0)) * (q^2)/(r^2)` (attactive)
where `epsi_(0)` is permittivity of free space .
As one charge is +ve and other is `-`ve .
`therefore` Direction of force is A to B .
Coulomb.s law in vector rotation, the electrostatic force on charge `q_1` due to charge `q_2`
`underset(1 to 2) (F) = (1)/(4 pi epsi_(0)) * (q_(1) q_(2))/(|r_(1) - r_(2)|^(3)) * (r_(1) - r_(2))`
Given , `q_(1) = + q` and `q_(2) = -q`
`therefore underset(1 to 2) (F) = (1)/(4 pi epsi_(0)) * (q^(2))/(|r_(1) - r_(2)|^(3)) * (r_(1) - r_(2))`
where `r_(1)` = position vector of charge `q_(1)` and `r_(2)` = position vector of charge `q_(2)`