An analogy between electromagnetism and hydrodynamics. Maxwell and Euler equations.

Analogy is a powerful tool of discovery. James Clerk Maxwell, in particular, used certain

analogies between hydrodynamics and electromagnetism to better understand the nature of the

electromagnetic field.

In this talk I shall present a formal analogy between Euler equations expressed in new meaningful

hydrodynamical variables and Maxwell equations. This formal analogy helps us to consider also some physical analogies between these two theories. An interesting question concerns the choice of

"the right variables' to describe a physical theory. Simple examples show that there are benefits but also subtle traps in using analogies.