Electric Charge and Coulomb's Law

A rubbed balloon picks up extra electrons from your hair, so it carries a net negative charge. Bring it near a wall and it pushes the wall's own electrons away, leaving the near surface slightly positive. Opposite charges attract, so the balloon sticks, even though the wall was never charged on purpose. That attraction, like every electric force between charges, obeys one rule: Coulomb's law. The force between two point charges is F = kq1q2/r², where k = 8.99 x 10⁹ N·m²/C², q1 and q2 are the charges in coulombs, and r is the distance between their centers. Bigger charges mean a bigger push or pull. Bigger distance means a much smaller one, because r is squared in the denominator. That squared term is the whole personality of the law: double the distance and the force doesn't drop to half, it drops to a quarter, since 1/2² = 1/4. Triple the distance and the force falls to a ninth.

When more than one charge acts on a target charge, treat each pair separately with Coulomb's law, then add the individual forces as vectors, since force has direction as well as size. A charge squeezed between two equal positive charges feels two pushes trying to shove it away from each side; if it sits exactly in the middle those pushes cancel and the net force is zero. Move it off center, or add a third charge to one side, and the forces no longer balance, so you have to track both magnitude and direction for every pair before combining them.

This pairwise force law sets up the next idea in the unit: instead of recomputing forces for every new charge you bring in, you can describe the space around a charge with an electric field, the force per unit charge waiting at each point, and build potential energy and potential from there.