Question

prove that electric field is conservative in nature?​

Answer 1

Answer:

If only the initial points and the final points are the source and not the path which is followed for the work which is done by the force for moving a particle from one point to the other.

We can prove that electric field is conservative in nature by taking line integration of the electric field along a close path which will be always zero thus the we will get that electric field does not depends on path but depends on the point which will be given.

Answer 2

A force is said to be conservative if it is independent of the path in which it travels and depends only on the initial and final points when travelling from one point to another

Considering line integral from point A to B

∫EdI {along a to b}

Considering line integral from point B to A

∫EdI {along B to A}

∫EdI {along a to b} = - ∫EdI {along b to a}

So total = ∫EdI {along a to b}+ ∫EdI {along B to A}  

=∫EdI {along a to b} - ∫EdI {along a to b}

=0