Two charges, one inverse square
Two charges at rest push or pull on each other, and the size of that push is Coulomb's law: — read aloud F equals k-e q-one q-two over r squared. Name every letter before it works for you. is the electrostatic force in newtons. and are the two charges in coulombs — the subscripts simply label them, one for each charge, and swapping which is which changes nothing, because they multiply. is the centre-to-centre separation in metres. And is Coulomb's constant, , which this chapter prints as the way every first-year text does. In this lesson the two charges and the separation are always given, and is what you are solving for.
The is the headline. Double the separation and the force falls to a QUARTER, not a half. Halve it and the force quadruples. Gravity does exactly the same thing with masses, which is not a coincidence — it is what a force spreading out over the surface of a sphere always looks like.
The real difficulty in this lesson is not the physics, it is the prefixes. A whole coulomb is a monstrous amount of charge; benchwork lives in microcoulombs, . Two of them multiplied together carry , and that tiny factor is the only thing standing between 's nine billion and an answer you could hold in your hand. Convert both charges before you touch the calculator, every single time.