Differential equations governing dynamic behavior of toroid-shaped ferro-magnetic material having a small gap of uniform width were derived incorporating Maxwell equations of electromagnetic induction relevent to the system and Newtonian equation of motion. Once the external uniform magnetic field was applied within the material through dc-circuit around the toroid, gap begin to change which lead to the abrupt variation of field in the material and gap according to the differential equations already derived. Characteristics of current and electromotive force with respect to time in the circuit consisting of inductance and resistance in series could be predicted from numerical solutions of these equations. As current in the circuit increasesl, magnetic field in the material increases, thus, the gap starts to shrink due to increased attractive force between gap and elastic restoring force in the material. With an appropriate selection of elastic constant of toroidal ferromagnetic material and design of gap structure it is possible to obtain the specified in both linear and nonlinear magnetic characteristics, such as current dependent and independent inductance.