Q.An electric field $\vec{E}=10\hat{i}\ \text{N C}^{-1}$ exists in a certain region of space. Then the potential difference $V=V_O-V_A$, where $V_O$ is the potential at the origin and $V_A$ is the potential at $x=2\ \text{m}$, is:

Conservative Nature of the Electrostatic Field

The electrostatic field is conservative: the work done by the electric force in moving a charge between two points depends only on the endpoints, never on the path taken. A direct consequence is that the work done around any closed loop is exactly zero:

Intuition: because the field can be written as the gradient of a potential, moving a charge and returning it to its start recovers all the energy spent — there is no net gain or loss. This is what lets us define a single-valued electric potential $V$ at each point. …