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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