## 9.1. Electromagnetic Models

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.

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