Explain electrostatic potential energy difference and give the noteworthy comments on it.

(N/A) At every point in an electric field,a particle with charge $q$ possesses a certain electrostatic potential energy. The work done by an external force in moving this charge increases its potential energy by an amount equal to the potential energy difference between points $R$ and $P$.
Thus,the potential energy difference is:
$\Delta U = U_{P} - U_{R} = W_{RP}$
Therefore,we can define the electric potential energy difference between two points as the work required to be done by an external force in moving (without acceleration) a charge $q$ from one point to another within the electric field of any arbitrary charge configuration.
Following comments may be made:
$(i)$ The work done depends only on the initial and final positions of the charge. It means that the work done by an electrostatic field in moving a charge from one point to another is independent of the path taken. This is the fundamental characteristic of a conservative force.
$(ii)$ The absolute value of potential energy is not significant; only the difference in potential energy is physically significant. If we add an arbitrary constant $\alpha$ to the potential energy at every point,the difference remains unchanged: $(U_{P} + \alpha) - (U_{R} + \alpha) = U_{P} - U_{R}$.
If we define the potential energy to be zero at infinity,then the work done in bringing a charge from infinity to a point $P$ is $W_{\infty P} = U_{P}$. Thus,the potential energy of a charge $q$ at a point is defined as the work done by an external force (equal and opposite to the electric field force) in bringing the charge $q$ from infinity to that point.