The force responsible for the movement of unit positive charge in the line integral of electric field?

Electric force of repulsion.

Hi Rameez,

To slowly move a unit positive charge, an external force must be applied which is same in magnitude but opposite in deirection of the electrostatic force. This is a direct implication of the way one calculates the potential and PE at a point in an electric field.

Wish you all the best.

Regards,

Ashwin (IIT Madras).