Doubts on properties of electric field lines

[gracy]

In my book following points have been given
1-due to conservative nature of electric field ,the electrostatic field lines will not form any closed loop.I want to ask how forming a loop makes if non conservative?
2-Field lines have tendency to contract in length (longitudinal contraction )like a stretched elastic string.The lateral pressure between field lines explains the mutual repulsion between like charge.This kind of imply electric field line possesses physical existence which they don't,do they?If not why such physical properties like contraction,pressure have been given to them in their description.
3-For electric field lines to be thee,the space/place should have electrostatic field,right?

 

[Titan97]

let's say there is a closed loop of electric field. If you place a positive charge on the loop, it feels a force qE. Due to this force,it moves along the loop and comes back to its initial position. But force due to electric field is parralel to displacement. Hence work done is non-zero while change in potential energy is zero. This means $W \neq -\Delta U$ which would make it non conservative.

 

[gracy]

qE is parralel to displacement

How?

 

[Titan97]

Post edited.

 

[Chandra Prayaga]

That is the definition of a non-conservative field. If the work done in taking a point charge around a loop is not zero, the electric field is called non-conservative.

 

[Let'sthink]

When Titan says displacement parallel to E ge means infinitesimal displacement at each point along the loop.