The article analyzes the macroscopic distribution of magnetic flux but the method proposed herein clarifies the microscopic behavior of local magnetic flux. Electromagnetic force at every time instant and the Joule's heat loss in the shading coil is analyzed in detail quantitatively. Hence, it has become possible to calculate the voltage-electromagnetic force characteristics. The effect of air-gap length between swing coil and fixed coil on the electromagnetic characteristics, a design problem for many years, has been analyzed clearly by the proposed method. The article applies the time periodic finite element method to an electromagnet with shading coil, which is used to operate switches.