The work is useful for a deep understanding of electromagnetics and hydrodynamics. The Navier-Stokes equation is derived for the evolution of magnetic field in the medium by using the Maxwell equations, Lorenz force and Ohm's law. The result shows that the magnetic induction intensity, current density, Lorenz force, superconductor boundary, Ohm's law and Ampere force in electromagnetics are analogous to the velocity, vorticity, Lamb vector, solid boundary, Newton's law of viscosity and Kutta-Joukowskis theorem of lift force in hydrodynamics, respectively. In the present work, the electromagnetic fields in a conducting medium are compared to the flow fields of an incompressible Newtonian fluid. However, this theory cannot make a correspondence of energy between two fields. Maxwell developed an analogy, where the magnetic field and the vector potential in electromagnetics are compared to the vorticity and velocity in hydrodynamics, respectively. The similarity between electromagnetics and hydrodynamics has been noticed for a long time. The new concepts introduced in this work suggest possible applications to electromagnetic propulsion devices and the mastery of the principles of producing electric fields of required configuration in plasma medium. It is shown how the intermingling between the fluid vector fields and electromagnetic fields leads to new insights on their dynamics. From this ground we offer a fluidic approach to different kinds of issues with interest in propulsion, e.g., the force exerted by a charged particle on a body carrying current the magnetic force between two parallel currents the Magnus force. This methodological approach allows us to give a general expression for the hydromotive force, thus reobtaining the Navier-Stokes equations by using the appropriate electromotive force. We develop a systematic approach establishing analogies between physical magnitudes and isomorphism (structure-preserving mappings) between systems of equations. We report on a new methodological approach to electrodynamics based on a fluidic viewpoint.
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