A two-dimensional forward problem formulation is introduced for electrical impedance tomography (EIT) using induced currents. The forward problem is linearised around a certain resistivity distribution and the inverse problem is formulated as a solution of a linear system of equations. Sensitivity of boundary measurements to resistivity variations arc analysed for spatially uniform, linear and quadratic fields. The formulation, however, is suitable for studying the effects of a general magnetic field applied to induce the currents in the conductive object. A similar inverse problem formulation is also developed for EIT using injected currents. Simulation studies are performed by reconstructing images of a simulation distribution using both methods separately with generalised inversion. It is also shown that the derived formulations for the inverse problems of the two methods can be combined to solve a larger set of equations with a greater number of independent measurements.