The equilibrium of an axisymmetric toroidal plasma, with almost circular cross-section, situated in an external magnetic multipole field is considered. The external field is created by a number of circular current carrying conductors symmetrically arranged outside of the plasma (Extrap configuration). The equilibrium field is expanded to first orders in the inverse aspect ratio and in a small parameter describing the non-circularity of the plasma cross-section. The current density is taken on the form j= kappa 2 psi +C. With this choice, both 'peaked' ( kappa 2>0) and 'skin-type' ( kappa 2<0) profiles can be described. The results obtained indicate that, in the range of parameters where equilibria with non-elongated magnetic surfaces ('square-shaped' separatrix) can be found, in the case of four external conductors, there is a high sensitivity of the plasma location (toroidal radius) to the precise values of the currents in the external conductors.