Please clarify doubt concerning potential enegry [closed]

Question

Let $W$ between two point be defined as: $$W=\int_a^b \vec{F}.\vec{dr}$$

Here $W$ is the work done between two fixed points $a$ and $b$.

Let $U$ at a point be defined as:

$$U_{\text{at } b}=\int \vec{F}.\vec{dr}+ \text{constant}$$

Here is it proper to say that potential energy $(U)$ is the work done between a fixed point $b$ and another arbitrary point. That is, can we say potential energy is work done having many degrees of freedom.

Answer 1

Potential at a point is indeed defined relative to an arbitrary reference. Once you define this reference, you should use it for all other points in the system.

Work between two points is the difference between potentials and is not dependent on reference choice.

Answer 2

Here potential energy of PARTICLES is the work done by me to put the particles one by one where they are. Potential energy of a particles is right