What makes potential energy in Coulumb's Law negative?

Question

So I understand that the formula for Coulomb's Law is F=kq1q2/d^2 or could also be written as V=kq1q2/d^2 where V is the potential energy. When I'm given a hypothetical atom that has 1 proton and 1 stationary electron, the potential energy is negative, yes? Since q1 and q2 are the charges of the particles, they are (-1)(1), representing one electron and one proton. However, in a situation where there is one electron and two protons, does the answer still come out as a negative? Since it'd still be (-1)(2)... I'm so confused on that because the charge of the proton is greater so shouldn't that indicate that the potential energy should be positive? Yet, the formula states to multiply the charges and that would get me a negative value most of the time.

Please help, I really don't understand this and it's making me so confused and frustrated right now.

Answer 1

Remember the work-energy theorem .. energy is transferred (J) when work is done (J), and the amount or energy transferred is equal to the amount of work done.



The ± is indicating how the work is done .. if an external force does the work (eg .. when lifting a load against gravity) there is a gain (+) in GPE. If the field (gravity) does the work as the object falls there is a loss (-) of GPE.

And so it is with Electrical PE .. where there has been attraction (ie .. between an -e and +p as they are brought together to form a neutral atom), the field does the work (no external force required) and there is a loss of EPE, so it's -V.



Bringing two protons or two electrons together (against their mutual repulsion) requires an external force to do the work .. and this increases the EPE of the pair (+V)



By this convention it doesn't matter how different in magnitude of the charges are .. all that matters is how the work has been done to move the charges.

Answer 2

It's about the relation BETWEEN the particles. Which one is considered positive and which one is considered negative is arbitrary. One charge by itself has no potential energy, positive or negative. So it's not about which kind of charge you have more of. It's the relationship between the charges.



When you have opposite charges, there will be an attractive force and negative potential energy. When you have like charges, there will be a repulsive force a positive potential energy. Would you think, if you have two negative charges, there should be negative potential energy, because clearly negative charge dominates? Nope. You will multiply the charges and get a positive. It doesn't matter that both are negative, it only matters that both are the same. Same charge: positive potential energy.



You will get the same potential energy in a situation with 2 protons and 1 electron or 1 proton and 2 electrons: negative in either case.

Answer 3

Whenever either q_1 or q_2 is negative. In case of an atom with two protons (q_1 = +2e) and one electron (q_2 = -e) the potential enegy is V(r) = k(+2e)(-e)/r the potential enery is negative. When the total energy which is kinetic energy plus potential energy is negative you have a system that is bound. That is you have supply plus that amount of enegry to make the system energy equal to zero, ie, to set the particles free of eachothers constraint.