and the ideal induction equation

In addition, there is the equation of mass continuity

and the remainder of Maxwell's equations

plus

and an

Note,

- In the equation of motion we have an extra magnetic force,
(the Lorentz force), that is normal to both the
magnetic field and the current. On using (4.5), this force may
be written in
the form

The second term on the right hand side represents a*magnetic pressure force*, , acting from regions of high magnetic pressure to low magnetic pressure. The first term is interpreted as a*magnetic tension force*which acts when the field lines are curved. Magnetic tension is similar to the force exerted by a stretched elastic band. Interpreting the Lorentz force in terms of these two basic quantities is important since it is possible to see how the plasma will respond to a given magnetic field configuration. - In the Maxwell equation,

which is called Ampère's Law, the last term is negligible, except for extremely rapid time variations. Dropping this term gives (4.5). In order of magnitude, the Maxwell equation,

which is called Faraday's Induction Law, can be approximated by , where and are typical time and length variations of the plasma. Comparing the left hand side with the last term (the displacement current) in Ampère's law, we find that

Thus,

where we have used

for the speed of light and the typical plasma velocity is . Hence, (4.5) is valid provided the plasma flows are small compared with the speed of light. - A plasma moving with a velocity experiences an
electric field
in addition to so
that Ohm's Law is

Normally, the left hand side is negligible so that (4.8) reduces to

Using (4.9) to eliminate the Maxwell equation

reduces to (4.2).