Electric potential/gravitational potential

Question

potential  is defined as the amount work done  by an external force  to move from something position at infinity to position R per unit charge
if the two charges are positive. then the potential energy between them represents the total amount of energy gained by charge q as the field does work on it as it moves through a distance of infinity from r
however if the charges are opposite, what does this potential energy actually represent? does it represent the total amount of kinetic energy that charge A ,COULD gain... like with the same charge case, or something different? i am only confused as in this scenario the two would attract and it would not move from r to a distance of infinity ( so the field wouldnt do the -potential energy of work back onto it)
i can grasp potential DIFFERENCE in the opposite charge case, but not just not what the potential function would represent in the different charge case.

YouFoundMe · Answer

To understand what the sign of Potential signifies it is enough to see that, work done $W=F.dr$ hence basically positive/negative work or potential simply represents the parallelness or antiparallelness between displacement and force that caused the displacement.
In case of oppositely charge body, they attract by Coulombs law and so the word done by an external source to bring one of the charge from infinity to $r$ is negative which means that external force is opposite to the displacement.
What does Potential Energy represent?
Potential energy represents the energy stored in the system that may or maynot be tapped into.
Now using Work Energy Theorem which is a consequence of conservation of energy that states,
$$W=Delta{K.E}$$ as you rightly said - change in Potential Energy has a direct effect on Kinetic Energy.

Electric potential/gravitational potential

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