The *induction equation* is derived by eliminating **E** from
Faraday's Law () and Ohm's Law (),
using (), () and a vector identity:

After making the above approximations,
the final set of MHD equations are the induction equation
and equations
(), and ()
with :

(3.44) |

(3.45) |

We now have one scalar and two vector equations in two scalar quantities
(,
** p**) and two vector
quantities (,
).
We thus require one more scalar equation to close the
set of equations. This can either be the energy conservation equation
()
or, as is commonly adopted, an equation of state for the fluid;
in this case the adiabatic equation of state ().