this thesis considers the effect of a magnetic field on the transition from a conducting to a non-conducting state in impurity semiconductors, with particular reference to indium antimonide. two models for such a transition have been proposed: one is based on the disappearance of bound states of the impurity due to screening by conduction electrons and the other is based on the onset of conduction due to overlap between the electron wave functions on adjacent impurity sites. the present work extends the latter model to include the effect of magnetic fields. the theoretical work of yafet, keyes and adams (ref. 6), fenton and haering (ref. 5) and durkan and march (ref. 10) is reviewed in section 2 of the thesis. in section 3 a dielectric approach to impurity conduction, due to frood (ref. 12), is introduced; he shows that the impurity system is non-conducting when (see document for formula) where n is the impurity concentration, a is the average polarizability of an impurity atom and cq is the dielectric constant of the background crystal. we use this criterion in section 4 to calculate a value of the critical magnetic field needed to make conduction cease, deriving a as a function of magnetic field from a variational calculation of the ground state energy of the impurity. our calculation is carried out for (see document for formula) so that the impurities are all in the ground state and there are no electrons in the conduction band (i.e. we do not consider excited states of the impurity or screening by conduction electrons). finally we compare theoretical predictions with published experimental results.