  The similarity between electromagnetics and hydrodynamics has been noticed
for a long time. Maxwell developed an analogy, where the magnetic field and the
vector potential in electromagnetics are compared to the vorticity and velocity
in hydrodynamics, respectively. However, this theory cannot make a
correspondence of energy between two subjects. In the present work, the
electromagnetic fields in a conducting medium are compared to the flow fields
of an incompressible Newtonian fluid. 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-Joukowski theorem of lift force in hydrodynamics, respectively. 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 work is
useful for a deep understanding of electromagnetics and hydrodynamics.

Fluid Dynamics