Magnetic Reynolds Number Calculator for eddy current braking

This template calculates the magnetic Reynolds number in the context of eddy current braking, which is measure of how well magnetic fields can diffuse (or spread out) within a conducting material, compared to how quickly the magnetic field is advected (or transported) by the conducting material.
CalculationInput﻿﻿μ
:1.0H/m​
﻿
﻿﻿σ
:1.0S/m​
﻿
﻿﻿v
:2.0m/s​
﻿
﻿﻿L
:2.0m​
﻿
Output﻿﻿Rm
:4.0​
﻿
﻿
Rm=μσvLRm=μσvLRm=μσvL
Where:
﻿﻿μ
 is the magnetic permeability, which is a measure of how easily a material can become magnetised in the presence of an external magnetic field. It has units in Henry per meter ﻿(H/m)
﻿
﻿﻿σ
 is the electrical conductivity, which is a measure of how easily a material can conduct electric current. It has units in Siemens per meter ﻿(S/m)
﻿
﻿﻿v
 is the characteristic velocity of the conductor relative to the magnetic field. It has units in meters per second ﻿(m/s)
﻿
﻿﻿L
 is the characteristic length scale of the conductor, such as its thickness or diameter. It has units in meters ﻿(m)
﻿
﻿﻿Rm
 is the magnetic Reynolds Number, a dimensionless quantity
💡What are the units Henry and Siemens?
ExplanationThe magnetic Reynolds number provides a measure of how well magnetic fields can diffuse (or spread out) within a conducting material, compared to how quickly the magnetic field is advected (or transported) by the conducting material.
What is eddy current braking?An eddy current brake is a device used to slow or stop a moving object by generating eddy currents and thus dissipating its kinetic energy as heat.
Eddy current braking utilises electromagnetic induction to generate resistive forces within a conductor. These resistive forces, known as eddy currents, oppose the motion of the conductor which produces a braking effect.
Eddy current braking has applications in various systems where controlled deceleration or stopping of moving objects is required, such as trains, roller coasters, and industrial machinery.
﻿
An example of an eddy current brake. [Source: Wikipedia]
The significance of the magnetic Reynolds Number in the context of eddy current braking is that when:
﻿﻿Rm<1
, the skin effects are negligible so the eddy current braking torque follows the theoretical curve of an induction motor
﻿﻿Rm>30
, the skin effects dominate and the braking torque decreases much slower with increasing speed than the induction motor model predicted
﻿
An eddy current brake, where a conductive disc rotates perpendicularly through a magnetic field. As the disc rotates, it induces eddy currents and power is dissipated throughout the disk to produce a braking torque force.
Related Resources Bernoulli Mass Flow Rate Calculator
Magnetic Reynolds Number Calculator
Reynolds Number Calculator
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