A model of low-frequency rotating magnetic field with a weak axial gradient

We introduce a model of rotating magnetic field with a weak axial gradient which approximates the field generated by a slightly conical and sufficiently long inductor. The axial variation of the free-space field is assumed to be weak and its amplitude is approximated by the first linear term of expansion in a power series of the axial coordinate. This allows us to obtain an analytic solution for the azimuthal harmonics of the induced scalar electric potential and the azimuthal driving force in a cylinder of finite length. The results are verified by comparison with a numerical solution obtained by a Chebyshev tau-method.