Non-contact actuated microbeads have attracted a lot of attention in recent years because of its enormous potential in medical, biological, and industrial applications. Researchers have proposed a multitude of electromagnetic actuation（EMA） systems consisting of a variety of coil pairs. However, a unified method to design and optimize a coil pair according to technical specifications still does not exist. Initially, this paper presented the modeling of an untethered ferromagnetic particle actuated by externally applied magnetic field. Based on the models, a simple method of designing and optimizing the EMA coil pair according to technical specifications, was proposed. A loop-shaped coil pair generating uniform magnetic and gradient fields was chosen to demonstrate this method clearly and practically. The results of the optimization showed that the best distance to radius ratio of a loop-shaped coil pair is 1.02 for a uniform magnetic field and 1.75 for a uniform gradient field. The applicability of the method to other shapes of coil configuration was also illustrated. The best width to distance ratio for a square-shaped coil pair is 0.558 and 0.958 for uniform magnetic and gradient fields, respectively. The best height to width ratio and distance to width ratio for a rectangle-shaped coil pair is h/w = [0.9,1.1], d/w = [0.5,0.6] for uniform magnetic field and h/w = [1.0,1.2], d/w = [0.9,1.1] for uniform gradient field. Furthermore, simulations of a microparticle tracking the targeted trajectory were conducted to analyze the performance of the newly designed coils. The simulations suggested the ability of manipulating microparticles via the coils designed by our proposed method. The research mainly proposed a unified design and optimization method for a coil pair, which can support researchers while designing a specific coil pair according to the technical requirements. This study is aimed at researchers who are interested in EMA system and microrobots.
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