for a conservative field ….....,,,,,.,.,. .,......

∫E.dl=?

Electrostatic forces are conservative in nature.When a unit positive test charge is moved from one point to another against a electrostatic field of positive line charge it undergoes repulsion due to like charges.Hence a certain amount of work is done to move the charge towards the positive line charge.When an external force does work in taking a body from one point to another against a force , then work gets stored as potential energy.Once when the force is removed the body moves , gaining kinetic energy and losing equal amount of potential energy .Thus the sum of kinetic and potential energy is conserved.Thus no work is done in moving a unit positive test charge over a closed path in an electric field.Mathematically ,we express this result as ,line integral of closed path in the electric field is always zero