Magnetic forces between arrays of cylindrical permanent magnets

Permanent magnet arrays are often employed in a broad range of applications: actuators, sensors, drug targeting and delivery systems, fabrication of self-assembled particles, just to name a few. An estimate of the magnetic forces in play between arrays is required to control devices and fabrication procedures. Here, we introduce analytical expressions for calculating the attraction force between two arrays of cylindrical permanent magnets and compare the predictions with experimental data obtained from force measurements with NdFeB magnets. We show that the difference between predicted and measured force values is less than 10%.