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In my book following points have been given

  1. Due to the conservative nature of electric field, the electrostatic field lines will not form a 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 somewhat implies electric field line possess physical existence which they don't, or do they? If not why have such physical properties like contraction and pressure been given to them in their description.
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  1. When the electric field is conservative this means that the circulation of the electric field around a closed loop is zero: $\oint_c\vec{E}.d\vec{l}=0$, this means that the work done on a charge is zero. This can never be the case if the field lines are closed loops: the field lines are tangent to the electric field vectors with the same strength in every point of the loop, so when the lines are closed, let's say concentric circles, the field looks something like this. Now imagine a charge q travelling along a circle of radius r once. The field will do work because the force will act in the same direction as the direction in wich the charge is traveling. So $\oint_c\vec{E}.d\vec{l}\neq0$, not an electrostatic field!
  2. I think you're book is trying to give an intuitive explanation to the the behaviour of the electric field as in the image I added. As you can see, the field lines in the center are travelling in an almost straight line when they are far away from the charges, but when they approach the charges, the field lines are closer to each other and they are each bent towards one of the two charges. It looks like the lines 'push' each other away when the 'pressure', the amount of field lines per area, rises. Like I said you should see this as an intuitive explanation and you really should be careful thinking making this analogy. Field lines are a way of representing the electric field and we can visualize them in experiments, so to me they are real in this sense, but 'physical existence' is really more of a philosophical question, you can also read this. Like charges
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