Example of closed loop have zero electric field
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Electric Field Lines do form closed loop if the field is produced by a time varying magnetic field. ... If a field line formed a closed loop, then each equation would equal zero because there would zero divergence of the electric field which mean that electric monopoles could not exist - which they do!
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Electric field lines are drawn by us for giving a form for what's happening around a charge configuration. ... If Electric field line were a closed loop, the displacement would always be parallel to the field and hence the work will always be positive. This means, work done by Coulomb force cannot be zero
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