The solution of electromagnetic hydrodynamic problems at the continuum level requires the solution of Maxwell’s equations. The fundamental equations are:
 | (9–1) |
 | (9–2) |
 | (9–3) |
 | (9–4) |
The Continuity equation (conservation of electric charge), which is a combination of the equations above, is:
 | (9–5) |
In the equations above:
is
the magnetic induction
is
the electric displacement
is
the electric field
is
the magnetic field
is
the current density
is the electric
charge density
To close this system of equations, constitutive relationships and a suitable set of boundary conditions must be included.