The potential difference is however independent of the choice of reference.

.......................(2.36)

We have mentioned that electrostatic field is a conservative field; the work done in moving a charge from one point to the other is independent of the path. Let us consider moving a charge from point P₁ to P₂ in one path and then from point P₂ back to P₁ over a different path. If the work done on the two paths were different, a net positive or negative amount of work would have been done when the body returns to its original position P₁. In a conservative field there is no mechanism for dissipating energy corresponding to any positive work neither any source is present from which energy could be absorbed in the case of negative work. Hence the question of different works in two paths is untenable, the work must have to be independent of path and depends on the initial and final positions.

Since the potential difference is independent of the paths taken, V_AB = - V_BA , and over a closed path,

.................................(2.37)

Applying Stokes's theorem, we can write:

............................(2.38)