The coupling between the fluid flow field and the magnetic field can be understood on the basis of two fundamental effects: the induction of electric current due to the movement of conducting material in a magnetic field, and the effect of Lorentz force as the result of electric current and magnetic field interaction. In general, the induced electric current and the Lorentz force tend to oppose the mechanisms that create them. Movements that lead to electromagnetic induction are therefore systematically braked by the resulting Lorentz force. Electric induction can also occur in the presence of a time-varying magnetic field. The effect is the stirring of fluid movement by the Lorentz force.

Electromagnetic fields are described by Maxwell’s equations:

(21–1)

(21–2)

(21–3)

(21–4)

where (Tesla) and (V/m) are the magnetic and electric fields, respectively, and and are the induction fields for the magnetic and electric fields, respectively. q () is the electric charge density, and () is the electric current density vector.

The induction fields and are defined as:

(21–5)

(21–6)

where and are the magnetic permeability and the electric permittivity, respectively. For sufficiently conducting media such as liquid metals, the electric charge density q and the displacement current are customarily neglected [459].

In studying the interaction between flow field and electromagnetic field, it is critical to know the current density due to induction. Generally, two approaches may be used to evaluate the current density. One is through the solution of a magnetic induction equation; the other is through solving an electric potential equation.