What decides how hard two charges push?

E1 showed you that charges push and pull. This one asks what decides how hard — and ends somewhere you may not expect.

This one needs equipment. E1 needed two balloons. This needs a bench setup, and the page cannot do it for you.

What this page is: your lab notebook. It holds your predictions so you cannot quietly revise them, and it does the arithmetic on your measurements. Every number in it will be one you measured.

You will need

Eight identical metal-coated balls, 20 mm across. Two to hang, six spare. Weigh them; they must match within about 5%.
Thread, 30 cm, both pieces the same length, hung from one point.
A millimetre ruler.
A plastic rod and a piece of wool — a PVC pipe, a plastic ruler or a comb, rubbed hard. Dry hair works too.
A dry day. Damp air drains the charge away while you are still measuring.

One setup rule matters more than it looks. The starting separation must be no more than 0.68 times the thread length. On 30 cm threads that is about 20 cm. Beyond that, the arithmetic this page does stops being accurate enough to answer the question. You will see why at the end.

Something you are entitled to know before you start.

Nobody has built this apparatus yet. The separations this page predicts come from the physics, not from anyone having stood at a bench and measured them. We think it will work; we have not watched it work. If you build it, send something back. Not whether you got the “right” answer. Send two times: how long the balls took to stop swinging, and how fast the charge drained away while you waited. If those two times turn out to be similar, this experiment cannot be done as described. We would rather find that out from you than pretend otherwise.

This one works best after E1 · What is charge?, which is where the ideas it leans on come from. You can carry on without it.

Your predictions lock once you commit them.