We present a low-energy Lagrangian of planar QED written in terms of the local field V(x), which is the order-parameter field for the Higgs-Coulomb phase transition. In this theory, the electric charge is topological and is quantized on the classical level.$ The relevant homotopy group is 1(scrM)=scrZ, where scrM=scrS1 is the manifold of degenerate vacuum states in the Coulomb phase. This vacuum degeneracy is due to spontaneous breaking of a global U(1) symmetry generated by magnetic flux. The electrically charged particles are topological defects of the field V(x). The Aharonov-Bohm effect is understood without use of gauge potential and is a consequence of the extended nature of the charged particles.