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This paper presents some reduced analytical expressions of the magnetic field produced by a thick coil with rectangular cross section. The expressions obtained have a fully analytical part and a semi-analytical one using elliptic integrals and a numerical integration. Our expressions are compared with the ones determined by Babic [1]. We discuss the computational cost and the accuracy of each approach. We demonstrate that our analytical model has both a lower computational cost than the one determined by Babic and a simpler form. Such expressions are also useful to calculate the self inductance of a thick coil. These formulations are suitable for the design of engineering applications involving air coils. All our analytical expressions are implemented in a program freely available online.
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Ravaud et al. (2010) studied this question.
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