Superposition and kinship with gravitation

What happens with several charges? The answer has a precious simplicity: the superposition principle. The total force on a charge is the vector sum of the forces exerted by each of the others, taken one by one.

   q feels :   F_total = F₁ + F₂ + F₃ + ...      (sum of vectors)

Each Coulomb force is computed separately, with its direction, then they are added like arrows. Nothing more: the charges do not interfere in their action, they add up. This principle lets us treat complex situations (a cloud of charges, a molecule) from the single law between two charges.

Let us end with a striking kinship. Compare Coulomb's law and Newton's gravitation:

   Coulomb :      F = k · q₁·q₂ / r²        (charges)
   Newton :       F = G · m₁·m₂ / r²        (masses)

Same structure, same 1/r² decrease. But two decisive differences. Gravity is only attractive (no negative mass), whereas electrostatics attracts or repels. And the gap in intensity is dizzying: between a proton and an electron, the electric force is about 10³⁹ times stronger than their gravitational attraction. That is why, at the scale of atoms, gravity is utterly negligible, and why it is Coulomb's law that shapes matter.