Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.