Learning Goal:

To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them.

Coulomb's law describes the force that two charged particles exert on each other $($by Newton's third law, those two forces must be equal and opposite$).$ The force $F_{21}$ exerted by particle $2($with charge $q_2)$ on particle $1($with charge $q_1)$ is proportional to the charge of each particle and inversely proportional to the square of the distance $r$ between them:

vec$(F{)}_{21}=\frac{k{q}_2{q}_1}{r^2}$hat$(r{)}_{21}$

where $k=\frac{1}{4lo{n}_0}$ and hat$(r{)}_{21}$ is the unit vector pointing from particle $2$ to particle $1.$ The force vector will be parallel or antiparallel to the direction of hat$(r{)}_{21},$ parallel if the product $q_1{q}_2>0$ and antiparallel if $q_1{q}_2<mn>0</mn>$; the force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign.