Modeling of the eddy currents with the consideration of the induced magnetic flux

Since the eddy current problem usually depends on the geometry of the moving conductive sheet and pole shape, there is no general method to find out its analytical solution. The analyses of the eddy current in a rotating disk with an electromagnet and an extended array are performed in the case of a time-invariant field to find the approximate analytical solution. As a method to solve the eddy current problem, firstly, the concept of Coulomb´s law and the mapping technique are introduced with consideration of the boundary condition. Secondly, the induced magnetic flux density is calculated in a lumped way by using Ampere´s law. Thirdly, the net magnetic flux density is defined by introducing the magnetic Reynolds number R_m which is the ratio of the induced magnetic flux density to the applied magnetic flux density from the electromagnet. Fourthly, the analyses are extended to a system with an extended array of two electromagnets. Finally, the braking torque is calculated by applying the Lorentz force law and the computed result is compared with the experimental one