It is an important property of electrostatic fields that the line integral of electric field,
depends only on the initial and final position and is independent of the path taken in going from A to B.
Consider two points A and B in the electrostatic field of a charge ‘q’ kept at origin.
The line integral is, therefore, seem to be independent of path connecting A and B. We can conclude that line integral of electrostatic field (does not depends upon the curve L1 or L2 ) depends only on the position vectors of the initial and final points.
For a closed curve the initial and final positions are the same. Hence
The line integral of electrostatic field over a closed path is zero; the electrostatic field is conservative in nature.
Consider the work done in displacing a unit positive charge through a distance 'dl' in the field;
Total work done, in moving a unit positive charge from A to B, then is
Thus line intergral of electric field represents the amount of work done is moving a unit positive charge, between two given points, in an electrostatic field.
This work done by the elctrostatic force, is path independent, as electrostatic force is conservative in nature. The concept of potential energy exists only in the case of conservative forces. When electrostatic force exists, between two or more point charges within system, we can assign a potential energy U to the system (due to two interaction of the point charges).
