The sum of all electromagnetic forces between different particles...

According to Newton's third law of motion, the electromagnetic force exerted by one particle on another is equal in magnitude and opposite in direction to the force exerted by the second particle on the first.

Mathematically, $\vec{F}_{ij} = -\vec{F}_{ji}$, where $\vec{F}_{ij}$ is the force on particle $i$ due to particle $j$.

When calculating the sum of all internal electromagnetic forces within a system of charged particles, these forces always occur in action-reaction pairs. The sum of all such pairs is exactly zero, since $\vec{F}_{ij} + \vec{F}_{ji} = 0$.

This cancellation depends only on the mutual interaction between the particles and holds true irrespective of the magnitudes or the signs of the charges involved.