Lorentz field electrical impedance tomography (LFEIT) is a newly proposed technique for imaging the conductivity of the tissues by measuring the electromagnetic induction under the ultrasound pressure field. In this paper, the theory and numerical simulations of the LFEIT are reported based on the general time dependent formulation. In LFEIT, a phased array ultrasound probe is used to introduce a current distribution inside a conductive body. The velocity current occurs, due to the movement of the conductive particles under a static magnetic field. In order to sense this current, a receiver coil configuration that surrounds the volume conductor is utilized. Finite Element Method (FEM) is used to carry out the simulations of LFEIT. It is shown that, LFEIT can be used to reconstruct the conductivity even up to 50% perturbation in the initial conductivity distribution.