Druyd:Knowledge

Electrical Mobility

Storyboard

>Model

ID:(1527, 0)

Stokes force

Equation

>Top, >Model

The resistance is defined in terms of the fluid viscosity and the sphere's velocity as follows:

$F_v = b v$

Stokes explicitly calculated the resistance experienced by the sphere and determined that viscosity is proportional to the sphere's radius and its velocity, leading to the following equation for resistance:

$F_v =6 \pi \eta r v$

$\pi$

3.1415927

$rad$

5057

$r$

Radius of a sphere

$m$

10331

$v$

Speed

$m/s$

6029

$F_v$

Viscose force

$N$

4979

$\eta$

Viscosity

$Pa s$

5422

ID:(4871, 0)

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

$F_v =6 \pi \eta r v$

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)

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

$F_v =6 \pi \eta r v$

the relationship is obtained

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

with mobility equal to

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

ID:(11998, 0)