A Simple Calculation Method for Center Magnetic Flux Density of a Magnetic Core Electromagnet With a Wide Air Gap

Generally, electromagnet equipment such as an electric transformer is designed with the air gap as narrow as possible for assuming that the magnetic flux in the air gap does not spread. Therefore, it is possible to calculate the magnetic flux density in the air gap of the electromagnet using the magnetic circuit theorem. However, some equipment requires a wide air gap to use the spatial magnetic field. In this case, the magnetic circuit theorem cannot design the electromagnet because of the spread of magnetic flux in the air gap. Then, it becomes difficult to estimate the magnetic reluctance of the wide air gap. Therefore, it is difficult to formulate the center magnetic flux density in the wide air gap. In this work, the authors assume that the wide air gap of the electromagnet can be assembled by an infinite length solenoid with the reverse magnetomotive force finite length solenoid. In this model, the magnetic flux density in the wide air gap can be formulated using the magnetic circuit and the Biot–Savart law. The proposed model was tested in comparison to the experimental results of test electromagnets. The result shows that the proposed model can be used in the engineering design of electromagnets with a wide air gap.