As we know that electrostatic force is a conservative force
so we can say by the condition of conservative force
here we can rearrange the above equation as
now integrate both sides
Now we know by the definition of work done by a force is given by
now work done by conservative force is given as
Now from above work done by electric field to move charge from one point to other is given as
so here work done is given as
so change in potential energy is given by work done