Circuits & Electrical Power · Coulomb's Law
Two charges, one inverse square
score 0

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: F=keq1q2r2F = \dfrac{k_e q_1 q_2}{r^2} — read aloud F equals k-e q-one q-two over r squared. Name every letter before it works for you. FF is the electrostatic force in newtons. q1q_1 and q2q_2 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. rr is the centre-to-centre separation in metres. And kek_e is Coulomb's constant, 8.99×109 Nm2/C28.99\times 10^{9}\ \mathrm{N\cdot m^2/C^2}, which this chapter prints as 9.00×1099.00\times 10^{9} the way every first-year text does. In this lesson the two charges and the separation are always given, and FF is what you are solving for.

The r2r^2 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, 1 μC=106 C1\ \mathrm{\mu C} = 10^{-6}\ \mathrm{C}. Two of them multiplied together carry 101210^{-12}, and that tiny factor is the only thing standing between kek_e's nine billion and an answer you could hold in your hand. Convert both charges before you touch the calculator, every single time.