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An idealized mathematical model of the magnetic field due to a ring head with a highly permeable underlayer is solved using Fourier analysis. Accurate Fourier coefficients are derived for a range of gap dimensions. The leading term of the resulting exact series is shown to be equivalent to a previously published approximation, but it is demonstrated that this term alone is not normally sufficient to predict the field accurately.>
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D.T. Wilton (1991) studied this question.
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