Analytical Method of Eddy-Current Field Induced by Moving Conductor in Gradient Magnetic Field

Electromagnetic field analyses of conductors moving in magnetic fields have been widely applied in scientific research and industrial production. In this article, an equivalent model is proposed to solve the eddy-current field of an arbitrarily shaped conductor moving in a gradient magnetic field. As an example, the analytical model of a spherical conductor moving axially with air-core cylindrical coils is solved. First, the induced eddy-current density inside the conductor ball is derived by using Ohm's law of a moving conductor. Next, the eddy current inside the conductor ball is equivalent to coaxial current loops and is regarded as an excitation source in the newly established boundary-value problem. Then in experiments, the induced voltages of the pickup coil are in good agreement with the theoretical values, which can verify the analytical methods and results of this article. Furthermore, the time difference between the zero-crossing points of the induced voltage curve is inversely proportional to the moving speed, and the amplitude of induced voltage is proportional to conductor conductivity. The analytical methods proposed in this article can be used to solve the eddy-current fields induced by arbitrarily shaped conductors moving in gradient magnetic fields directly and do not need to calculate the governing equations and boundary conditions containing velocity terms.