show that electric field is conservative?

Dear Student

A detail mathematical proof of conservative nature of electrostatic force cannot be given at your level; a semi-qualitative idea is given below. 

Let us consider a positive charge +Q be and in its field let another +ve charge q be placed at a point A. Let point A be situated at a distance and let the field do a work W in displacing the charge q from A to B. Now there exists two path first the yellow path which is the shortest possible path another is the white path. See fig.

Now work done in displacing the charge q from A to B along yellow path will be

Again work done in displacing the charge along the white path from A to B will also be same because work done is force multiplied with displacement and displacement of the charge taken along the white path is also the straight yellow line along A to B.

Thus,  

Thus we see

or work done by the electrostatic force along both the paths is same.  

Thus, work done by the electrostatic force is independent of path between two points. Thus electrostatic force is conservative

 

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