  We present an exactly soluble charged wormhole model in two dimensions by
adding infalling chiral fermions on the static wormhole. The infalling energy
due to the infalling charged matter requires the classical back reaction of the
geometry, which is solved by taking into account of the nontrivial nonchiral
exotic energy. Finally, we obtain the exact expression for the size of the
throat depending on the total amount of the infalling net energy and discuss
the interesting transition from the AdS spacetime to the wormhole geometry.
