Is electric potential energy measured in absolute value?

Question

Is the formula for electric potential energy ($U = kqQ/r$) measured in absolute value? In other words, as the magnitude of $U$ increases, does electric potential energy increases too? For example, if $q<0$ and $Q>0$, as either one of them increase in magnitude, such as when $q$ becomes more negative, the magnitude of $U$ increases but it gets more negative. So does that mean electric potential energy increases as $q$ or $Q$ increases?

In another sense, if $q<0$ and $Q>0$, as $r$ increases: the magnitude of $U$ decreases (becomes less negative). So does electric potential energy decrease when r increases?

What approach do we take when looking at electric potential? The number line approach or the absolute value approach?

($U$ is potential energy, $k$ is a constant, $q$ and $Q$ are electric charge, and $r$ is the distance between $q$ and $Q$)

Answer 1

In another sense, if q<0 and Q>0, as r increases: the magnitude of U decreases (becomes less negative). So does electric potential energy decrease when r increases?

A value becoming less negative means that value is increasing.

This makes sense, since to separate two opposite charges you have to apply a force in the same direction as you're trying to move the charges. This means you're doing work on the system, and increasing its potential energy.

Answer 2

The formula that you have quoted $U=k\frac{qQ}{r}$is the potential energy of two charges $Q$ and $q$ where there separation is $r$ and the potential energy is zero when the separation of the charges is infinite.

The sign that you assign to the charges is important and their product of the charges with signs included will produce a potential energy on a number line.

So if the two charges have the same sign an external force has to do work to bring the two charges from an infinite separation to a separation of $r$.
This means that the system of two charges has more potential energy (it is positive, greater than zero) when their separation is $r$ compared with their separation being infinite.

If the charges have opposite signs an external force needs to do work in separating the charges from $r$ to infinity thus the potential energy of the system is greater when separation of the charges is infinite than when their separation is $r$.
Since the potential energy of the two charges is zero at infinite separation the potential energy at separation $r$ must be negative.

A potential energy of $-100\,\rm J$ is lower than a potential energy of $+100\,\rm J$ and the difference is $200\,\rm J$.