When a conducting plate moves through a nonuniform magnetic field, electromotive forces are induced in the conducting plate. According to Fleming's right-hand rule and left-hand rule, the induced currents produce a magnetic drag force. In these rules, a magnetic field perpendicular to the direction of movement generates a magnetic damping force. In the present work, we provide a possible resolution to the modeling of moving-conductor type eddy current dampers, using infinitesimal loop coils. Our model has three advantages: the equation of the magnetic damping force is simple; we can use the static magnetic field obtained by using the finite element method (FEM), the Biot-Savart law or experiments; and the model automatically satisfies boundary conditions. Using infinitesimal loop coils, we have modeled the magnetic damping force produced by a moving-conductor type eddy current damper composed of electromagnets and a conducting disk. Furthermore, the experimental setup has been fabricated, and damping ratios from experiments are compared to the analytical results and are found to be in good agreement with them.