Overview
Coulombs law specifies the force on one charge exerted by a second charge. It is experimentally determined to be
{% \vec{F} = \frac{1}{4 \pi \epsilon_0} \frac{q Q }{r^2} \hat{r} %}
From Netwons third law, the force experienced by other particle is the opposite of the force exerted on the first.
{% \vec{F}_{12} = - \vec{F}_{21} %}
Superposition Principle
The Superposition principle asserts that the total electromagnetic force experienced by a particle is the vector sum of the individual forces felt from each charged particle.
{% \vec{F} = \frac{Q}{4 \pi \epsilon_0} \sum_i \frac{q_i }{r^2} \hat{r} %}