Prove that electrostatic forces are conservative in nature and define electrostatic potential energy.

(N/A) force is conservative if the work done by it in moving a particle between two points is independent of the path taken. For an electrostatic force,the work done in moving a charge $q$ from point $A$ to point $B$ is $W = -(U_B - U_A)$,which depends only on the initial and final positions. Since the work done in a closed loop is zero,electrostatic forces are conservative.
Electrostatic potential energy is defined as: The work done by an external agent in bringing a unit positive charge from infinity to a specific point in an electric field at a constant speed (without acceleration) is defined as the electrostatic potential energy at that point.