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This paper addresses the interaction between plasma and a magnetic field rotating with uniform an angular velocity and amplitude. For our analysis, we assume a plasma with infinite conductivity and constant viscosity coefficients. Starting from the basic equations, we search for exact solutions with respect to velocity and magnetic field. Then, we study the stability of the exact solution and the behavior of these fields with respect to infinitesimal perturbations, presenting the results and discussing the influence of the Reynolds and magnetic numbers on the perturbed fields. We show that there is a change of normal mode of the perturbation fields via a linear relation between the Reynolds and magnetic numbers. In addition, we show the existence of undamped mode.