  Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have
investigated the properties of electron gas inside two-dimensional (2D)
Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic
field. The electron-electron Coulomb exchange interaction in quasi-2D case is
obtained. The exact form of exchange term in 2D is derived making the width of
the system tending to zero. Further, using the exchange term, the
Thomas-Fermi-Dirac equation in 2D is established. It has been observed that
only the ionized WS cell can have finite radius in the Thomas-Fermi model, even
in presence of a strong quantizing magnetic field. On the other hand, in the
Thomas-Fermi-Dirac model a neutral WS cell can have finite radius.
