Editing Magnetohydrodynamic drive (section)

== Principle ==
{{Main|Lorentz force}}
{{see also|Magnetohydrodynamic converter}}
[[File:Right hand rule cross product F=J×B.svg|thumb|Illustration of the right-hand rule for the Lorentz force, cross product of an electric current with a magnetic field.]]

The working principle involves the acceleration of an electrically conductive [[fluid]] (which can be a [[liquid]] or an [[Ionization|ionized]] [[gas]] called a [[Plasma (physics)|plasma]]) by the [[Lorentz force]], resulting from the [[cross product]] of an [[electric current]] (motion of [[charge carrier]]s accelerated by an [[electric field]] applied between two [[electrode]]s) with a [[perpendicular]] [[magnetic field]]. The Lorentz force accelerates all [[charged particles]], positive and negative species (in opposite directions). If either positive or negative species dominate the vehicle is put in motion in the opposite direction from the net charge.

This is the same working principle as an [[electric motor]] (more exactly a [[linear motor]]) except that in an MHD drive, the solid moving [[Rotor (electric)|rotor]] is replaced by the fluid acting directly as the [[propellant]]. As with all [[Electromagnetism|electromagnetic]] devices, an MHD accelerator is reversible: if the ambient [[working fluid]] is moving relatively to the magnetic field, [[Electric dipole moment|charge separation]] induces an [[voltage|electric potential difference]] that can be harnessed with [[electrode]]s: the device then acts as a [[Electric generator|power source]] with no moving parts, transforming the [[kinetic energy]] of the incoming fluid into [[electricity]], called an [[Magnetohydrodynamic generator|MHD generator]].

[[File:MHD converters (generator and accelerator).svg|thumb|512px|Crossed-field magnetohydrodynamic converters (linear Faraday type with segmented electrodes). A: MHD generator mode. B: MHD accelerator mode.|center]]

As the Lorentz force in an MHD converter does not act on a single isolated charged particle nor on electrons in a solid [[Electrical wiring|electrical wire]], but on a continuous [[Charge density|charge distribution]] in motion, it is a "volumetric" (body) force, a force per unit volume:

:<math>\mathbf{f} = \rho \mathbf{E} + \mathbf{J} \times \mathbf{B}\,\!</math>

where '''f''' is the ''force density'' (force per unit volume), ''ρ'' the [[charge density]] (charge per unit volume), '''E''' the [[electric field]], '''J''' the [[current density]] (current per unit area) and '''B''' the [[magnetic field]].{{clarify|date=July 2020}}