The following approximations are made to produce a tractable set of equations:

- 1.
- The displacement current term in Ampere's law ()
is omitted. This can be justified by comparing the LHS of ()
with the displacement current term:

where*L*and are the characteristic MHD length and time scales. Thus,

where from Faraday's law (). Hence () reduces to

- 2.
- Charge neutrality ()
is typically satisfied
in a plasma because the forces associated
with any unbalanced charges imply a potential energy per particle
that well exceeds the mean thermal energy per particle.
The charge conservation equation () then reduces to

This also follows by taking the divergence of equation (). - 3.
- The approximation () or () to Ohm's law is assumed.