# Potential energy mutually shared

Given there are $$2$$ non-moving like charges in space. the total energy is the sum of potential energies plus kinetic (zero).

The potential energy of charge $$A$$ due to charge $$B$$ is $$kq_1q_2/r$$ and the potential energy of charge $$B$$ due to charge $$A$$ is the same, then is the total energy twice the value we have calculated or it is just $$kq_1q_2/r$$?

It's just $$U=\frac{1}{4\pi \epsilon_0}\frac{q_1q_2}{r}$$ because the potential energy is associated with system not to individual charge.
In another word, we define the potential energy of a system of charges as the work necessary to bring them in from infinity. Thus We just have to do work in bringing $$q_1$$ near the $$q_2$$ or vice versa.
The electrostatic potential energy, $$U_E$$, of one point charge $$q$$ at position $$r$$ in the presence of an electric field $$E$$ is defined as the negative of the work $$W$$ done by the electrostatic force to bring it from the reference position to that position $$r$$. $$U_E(r)=-W_{r_{ref}{\to}r}=-\int_r^{r_{ref}}{qE(r').dr'}$$
The potential energy is $$k q_1 q_2 \over r$$, or $${1 \over 4 \pi \epsilon_0} {q_1q_2 \over r}$$ if you prefer: it does not 'belong' to A or B individually but to the joint AB system. You can't ascribe potential energy to individual objects in the same way that you can for kinetic energy.