Electrical Mobility

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>Model

ID:(1527, 0)

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Stokes force

Equation

>Top, >Model

The Stokes force is the force generated by the flow around a sphere immersed in it. In this case, the model of force proportional to velocity is used:

$ F = b v $

In this context, it can be shown that the constant $b$ is equal to:

$b = 6\pi r \eta$

where $r$ is the radius of the sphere and $\eta$ is the viscosity of the medium. Thus, the Stokes force is given by:

This force is primarily applicable in laminar flows.

ID:(4871, 0)

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Particle velocity in electric field

Equation

>Top, >Model

A charged particle q in an electric field \ vec {E} means that a force equal to

$ F = q E $

This force is opposed by a force due to the effect of the medium that can be modeled by Stokes law

$ F =6 \pi \eta r v_c $

If both forces are equalized, it is obtained that the particle moves with a constant speed equal to

$ \vec{v} = \mu \vec{E} $

with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$

ID:(11997, 0)

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Particle mobility in electric field

Equation

>Top, >Model

To equalize the force caused by the electric field

$ F = q E $

with the opposing force that is modeled with Stokes law

$ F =6 \pi \eta r v_c $

the relationship is obtained

$ \vec{v} = \mu \vec{E} $

with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$

ID:(11998, 0)

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