We study theoretically charged excitons ('hole + N electrons') in a double
quantum well with a metal gate in a magnetic field. In this system the inte
raction between the hole and the electrons can be approximated by a parabol
ic potential. We find the spectrum of far-infrared absorption by charged ex
citons and show how the Kohn's theorem in quantum dots can be extended to t
he case of a system with a finite total mass. In the case of the N-electron
exciton in a quantum ring, the exciton energy oscillates as a function of
the magnetic flux with a period that depends on N and the ratio of the mass
es. (C) 1998 Published by Elsevier Science B.V. All rights reserved.