A new and exact solution for the magnetic field of a thin film recording head in the presence of a high permeability magnetic underlayer is presented. Typical Fourier coefficients and corresponding fields are given. The leading term alone of the Fourier solution is shown to be more accurate than other previously published approximations when used in conjunction with an integral representation. A novel proposal of variable pole potential is analyzed in a similar manner and significant improvements in peak field strength, field gradients and the absence of secondary field peaks are demonstrated and quantified.
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