Abstract A theoretical investigation has been made of the electrical conductivity of an impurity band in an inversion layer in an external magnetic field. The specific case of an n-type inversion layer on a (100) surface of silicon is considered. A distribution of impurity ions is assumed to exist at the interface between the inversion layer and the oxide. Results are obtained for several values of the electric field in the inversion layer and for the two-dimensional limit corresponding to zero inversion layer thickness. Contact is made with the experimental results of Hartstein, Fowler and Woo.