Cat + Packing Peanuts

https://commons.wikimedia.org/wiki/File:Cat_demonstrating_st...

> But it's not at all obvious to me why the exponent a is 1 in nature

i think we can rule out any exponent just by dimensional analysis if you allow powers of q, then K has ambiguous units. Same reason you cant exponentiate unitful quantities

More specifically I think we can rule out even exponents by anti-symmetry of charge. That is q^2n = (-q)^2n which know is ruled out by experiment.

> Supposedly, one way to make two equal charges is to charge one thing and then put it in contact with the other thing, so that the charge splits by symmetry. But then how would we check that indeed we have two equally charged things?

same as with making guaranteed flat surface - you make 3 and measure each pair