Dirac strings in spin ices are lines of reversed dipoles joining two quasiparticle excitations. These excitations behave as unbound emergent monopoles if the tension of Dirac strings vanishes. In this Letter, analytical and numerical analysis are used to study the dynamics of two-dimensional dipolar spin ices, artificially created analogs of bulk spin ice, in the regime of bound monopoles. It is shown that, in this regime, strings, rather than monopoles, are effective degrees of freedom explaining the finite-width band of Pauling states. A measurable prediction of path-time dependence of endpoints of a stretched and, then, released Dirac string is made and verified via simulations. It is shown that string dynamics is defined by the characteristic tension-to-mass ratio, which is determined by the fine structure constant and lattice dependent parameter. It is proposed to use string tension to achieve spontaneous magnetic currents. A concept of an energy storing device on the basis of this principle is proposed and illustrated by an experimental demonstration. A scheme of independent measurement at the nanoscale is proposed.