1. The problem statement, all variables and given/known data There are n isolated condutoctors in space: Sum of charge of all conductors is positive. Show that surface density is postivie everywhere on at least one of conductors 2. Relevant equations Using induction 3. The attempt at a solution -It's clear that if we have one conductor with postive charge that it will have positive surface densitiy everywhere on its surface. But let's have a look on a problem in which we have one positive conductor (with charge q1) and let's say one negative (with charge -q2) where |q1|>|q2|. Charge on each of conductors will redistribute so that the electric field inside of it is 0 (electrostatic influence), it will redistribute in that way that positive charges of conductor1 will be attracted by negativ conductor1 and vice versa.I don't see a reason why shouldn't there be a negative surface charge on some part of the positive conductor due to this redistribution. -My idea for solving this was to use induction 1)I aready said that it's clear that for n=1 statment is correct 2) let's say that for some n of conductors at least one have positive surface charge everywhere 3)now let's try to add one more conductor to this system and show that at least one conductor will have positive surface area everywhere Unfortunately I don't know how to show that...perhaps there is some other way for solving this problem.