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In this paper, we numerically study the influence of the speed variation of a magnetic source on the distribution of current density, magnetization, and dissipated energy of a high-temperature superconducting cylinder described by a Jn power law. The results presented come from the resolution of a nonlinear diffusion problem of electric field by a mixed finite-element finite-volume discretization method. This method is robust, stable, and converges for large values of n. The calculations carried out for n, varying from 1 to 200, show that when the external magnetic field quickly varies from 0 to its maximal value, the maximum values of penetration, the magnetization, and the energy dissipation are obtained when the switching of magnetic field occurs. For a periodic magnetic field, we note that any change of the period results in variation of the magnetization and the dissipated energy.