# Magnetic Reynolds number (relationship to eddy current braking)

## Description

The dimensionless magnetic Reynolds number, is also used in cases where there is no physical fluid involved.

The magnetic Reynolds number is the magnetic analogue of the Reynolds number, a fundamental dimensionless group that occurs in magnetohydrodynamics. It gives an estimate of the relative effects of advection or induction of a magnetic field by the motion of a conducting medium, often a fluid, to magnetic diffusion.

The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory. When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case focus instead often rests on the influence of the magnetic field on the flow.

Related formulas## Variables

R_{m} | Magnetic Reynolds number (dimensionless) (dimensionless) |

μ | magnetic permeability (m^2/s) (dimensionless) |

σ | electrical conductivity (Plasma conductivity) (S/m) (dimensionless) |

L | characteristic length (m) (dimensionless) |

v | characteristic velocity (m/s) (dimensionless) |