I was revising Electric Fields and it came up that if a positive charge moves in the direction of the electric field (so away from a positive charge), then the electric potential energy will decrease but if the charge is negative, it will increase.
This adds up when you consider work has to be done on the negative charge to move it against the attractive in this case whereas, for the positive charge, the potential energy is used to work.
However, looking at it from another perspective using $E=kQq/r$, the potential energy will decrease with separation regardless of the charge. Most people answer this kind of question by bringing in the sign but I want someone to conceptually answer this problem:
We know that two charges have the maximum magnitude of Electric Force when they are closest together, whether attractive or repulsive. That means they will have maximum potential to accelerate under this force by $F=ma$. Maximum potential to accelerate means maximum Potential Energy that can be converted into Kinetic Energy. Since Energy is scalar, the direction does not matter here.
Please let me know what is wrong with the above assessment so that I may understand why the topmost paragraph stands true.
Edit: Can I get an answer that debunks my explanation in bold which is contradicting the quantitative answer.
Best Answer
If $\text{potential energy}=kQq/r$ and $Qq>0$ then as $r$ increases the potential energy decreases but if $Qq<0$ then as $r$ increases the potential energy increases by becoming less negative with the increase in $r$.